Non equivalent ints

Two n-digit integers are said to be equivalent if one is a permutation of the other. Find the number of 5-digit integers such no two are equivalent. If the digit 5,7,9 can appear at most one, how many non-equivalent five-digit integers are there?

Correct answer:

x =  1371

Step-by-step explanation:

x1=10000 x2=10001 x3=10002 x4=10003 x5=10004 x6=10005 x7=10006 x8=10007 x9=10008 x10=10009
x11=10011 x12=10012 x13=10013 x14=10014 x15=10015 x16=10016 x17=10017 x18=10018 x19=10019 x20=10022
x21=10023 x22=10024 x23=10025 x24=10026 x25=10027 x26=10028 x27=10029 x28=10033 x29=10034 x30=10035
x31=10036 x32=10037 x33=10038 x34=10039 x35=10044 x36=10045 x37=10046 x38=10047 x39=10048 x40=10049
x41=10056 x42=10057 x43=10058 x44=10059 x45=10067 x46=10068 x47=10069 x48=10078 x49=10079 x50=10088
x51=10089 x52=10099 x53=10111 x54=10112 x55=10113 x56=10114 x57=10115 x58=10116 x59=10117 x60=10118
x61=10119 x62=10122 x63=10123 x64=10124 x65=10125 x66=10126 x67=10127 x68=10128 x69=10129 x70=10133
x71=10134 x72=10135 x73=10136 x74=10137 x75=10138 x76=10139 x77=10144 x78=10145 x79=10146 x80=10147
x81=10148 x82=10149 x83=10156 x84=10157 x85=10158 x86=10159 x87=10167 x88=10168 x89=10169 x90=10178
x91=10179 x92=10188 x93=10189 x94=10199 x95=10222 x96=10223 x97=10224 x98=10225 x99=10226 x100=10227
x101=10228 x102=10229 x103=10233 x104=10234 x105=10235 x106=10236 x107=10237 x108=10238 x109=10239 x110=10244
x111=10245 x112=10246 x113=10247 x114=10248 x115=10249 x116=10256 x117=10257 x118=10258 x119=10259 x120=10267
x121=10268 x122=10269 x123=10278 x124=10279 x125=10288 x126=10289 x127=10299 x128=10333 x129=10334 x130=10335
x131=10336 x132=10337 x133=10338 x134=10339 x135=10344 x136=10345 x137=10346 x138=10347 x139=10348 x140=10349
x141=10356 x142=10357 x143=10358 x144=10359 x145=10367 x146=10368 x147=10369 x148=10378 x149=10379 x150=10388
x151=10389 x152=10399 x153=10444 x154=10445 x155=10446 x156=10447 x157=10448 x158=10449 x159=10456 x160=10457
x161=10458 x162=10459 x163=10467 x164=10468 x165=10469 x166=10478 x167=10479 x168=10488 x169=10489 x170=10499
x171=10567 x172=10568 x173=10569 x174=10578 x175=10579 x176=10588 x177=10589 x178=10599 x179=10678 x180=10679
x181=10688 x182=10689 x183=10699 x184=10788 x185=10789 x186=10799 x187=10888 x188=10889 x189=10899 x190=10999
x191=11111 x192=11112 x193=11113 x194=11114 x195=11115 x196=11116 x197=11117 x198=11118 x199=11119 x200=11122
x201=11123 x202=11124 x203=11125 x204=11126 x205=11127 x206=11128 x207=11129 x208=11133 x209=11134 x210=11135
x211=11136 x212=11137 x213=11138 x214=11139 x215=11144 x216=11145 x217=11146 x218=11147 x219=11148 x220=11149
x221=11156 x222=11157 x223=11158 x224=11159 x225=11167 x226=11168 x227=11169 x228=11178 x229=11179 x230=11188
x231=11189 x232=11199 x233=11222 x234=11223 x235=11224 x236=11225 x237=11226 x238=11227 x239=11228 x240=11229
x241=11233 x242=11234 x243=11235 x244=11236 x245=11237 x246=11238 x247=11239 x248=11244 x249=11245 x250=11246
x251=11247 x252=11248 x253=11249 x254=11256 x255=11257 x256=11258 x257=11259 x258=11267 x259=11268 x260=11269
x261=11278 x262=11279 x263=11288 x264=11289 x265=11299 x266=11333 x267=11334 x268=11335 x269=11336 x270=11337
x271=11338 x272=11339 x273=11344 x274=11345 x275=11346 x276=11347 x277=11348 x278=11349 x279=11356 x280=11357
x281=11358 x282=11359 x283=11367 x284=11368 x285=11369 x286=11378 x287=11379 x288=11388 x289=11389 x290=11399
x291=11444 x292=11445 x293=11446 x294=11447 x295=11448 x296=11449 x297=11456 x298=11457 x299=11458 x300=11459
x301=11467 x302=11468 x303=11469 x304=11478 x305=11479 x306=11488 x307=11489 x308=11499 x309=11567 x310=11568
x311=11569 x312=11578 x313=11579 x314=11588 x315=11589 x316=11599 x317=11678 x318=11679 x319=11688 x320=11689
x321=11699 x322=11788 x323=11789 x324=11799 x325=11888 x326=11889 x327=11899 x328=11999 x329=12222 x330=12223
x331=12224 x332=12225 x333=12226 x334=12227 x335=12228 x336=12229 x337=12233 x338=12234 x339=12235 x340=12236
x341=12237 x342=12238 x343=12239 x344=12244 x345=12245 x346=12246 x347=12247 x348=12248 x349=12249 x350=12256
x351=12257 x352=12258 x353=12259 x354=12267 x355=12268 x356=12269 x357=12278 x358=12279 x359=12288 x360=12289
x361=12299 x362=12333 x363=12334 x364=12335 x365=12336 x366=12337 x367=12338 x368=12339 x369=12344 x370=12345
x371=12346 x372=12347 x373=12348 x374=12349 x375=12356 x376=12357 x377=12358 x378=12359 x379=12367 x380=12368
x381=12369 x382=12378 x383=12379 x384=12388 x385=12389 x386=12399 x387=12444 x388=12445 x389=12446 x390=12447
x391=12448 x392=12449 x393=12456 x394=12457 x395=12458 x396=12459 x397=12467 x398=12468 x399=12469 x400=12478
x401=12479 x402=12488 x403=12489 x404=12499 x405=12567 x406=12568 x407=12569 x408=12578 x409=12579 x410=12588
x411=12589 x412=12599 x413=12678 x414=12679 x415=12688 x416=12689 x417=12699 x418=12788 x419=12789 x420=12799
x421=12888 x422=12889 x423=12899 x424=12999 x425=13333 x426=13334 x427=13335 x428=13336 x429=13337 x430=13338
x431=13339 x432=13344 x433=13345 x434=13346 x435=13347 x436=13348 x437=13349 x438=13356 x439=13357 x440=13358
x441=13359 x442=13367 x443=13368 x444=13369 x445=13378 x446=13379 x447=13388 x448=13389 x449=13399 x450=13444
x451=13445 x452=13446 x453=13447 x454=13448 x455=13449 x456=13456 x457=13457 x458=13458 x459=13459 x460=13467
x461=13468 x462=13469 x463=13478 x464=13479 x465=13488 x466=13489 x467=13499 x468=13567 x469=13568 x470=13569
x471=13578 x472=13579 x473=13588 x474=13589 x475=13599 x476=13678 x477=13679 x478=13688 x479=13689 x480=13699
x481=13788 x482=13789 x483=13799 x484=13888 x485=13889 x486=13899 x487=13999 x488=14444 x489=14445 x490=14446
x491=14447 x492=14448 x493=14449 x494=14456 x495=14457 x496=14458 x497=14459 x498=14467 x499=14468 x500=14469
x501=14478 x502=14479 x503=14488 x504=14489 x505=14499 x506=14567 x507=14568 x508=14569 x509=14578 x510=14579
x511=14588 x512=14589 x513=14599 x514=14678 x515=14679 x516=14688 x517=14689 x518=14699 x519=14788 x520=14789
x521=14799 x522=14888 x523=14889 x524=14899 x525=14999 x526=15678 x527=15679 x528=15688 x529=15689 x530=15699
x531=15788 x532=15789 x533=15799 x534=15888 x535=15889 x536=15899 x537=15999 x538=16788 x539=16789 x540=16799
x541=16888 x542=16889 x543=16899 x544=16999 x545=17888 x546=17889 x547=17899 x548=17999 x549=18888 x550=18889
x551=18899 x552=18999 x553=19999 x554=20000 x555=20002 x556=20003 x557=20004 x558=20005 x559=20006 x560=20007
x561=20008 x562=20009 x563=20022 x564=20023 x565=20024 x566=20025 x567=20026 x568=20027 x569=20028 x570=20029
x571=20033 x572=20034 x573=20035 x574=20036 x575=20037 x576=20038 x577=20039 x578=20044 x579=20045 x580=20046
x581=20047 x582=20048 x583=20049 x584=20056 x585=20057 x586=20058 x587=20059 x588=20067 x589=20068 x590=20069
x591=20078 x592=20079 x593=20088 x594=20089 x595=20099 x596=20222 x597=20223 x598=20224 x599=20225 x600=20226
x601=20227 x602=20228 x603=20229 x604=20233 x605=20234 x606=20235 x607=20236 x608=20237 x609=20238 x610=20239
x611=20244 x612=20245 x613=20246 x614=20247 x615=20248 x616=20249 x617=20256 x618=20257 x619=20258 x620=20259
x621=20267 x622=20268 x623=20269 x624=20278 x625=20279 x626=20288 x627=20289 x628=20299 x629=20333 x630=20334
x631=20335 x632=20336 x633=20337 x634=20338 x635=20339 x636=20344 x637=20345 x638=20346 x639=20347 x640=20348
x641=20349 x642=20356 x643=20357 x644=20358 x645=20359 x646=20367 x647=20368 x648=20369 x649=20378 x650=20379
x651=20388 x652=20389 x653=20399 x654=20444 x655=20445 x656=20446 x657=20447 x658=20448 x659=20449 x660=20456
x661=20457 x662=20458 x663=20459 x664=20467 x665=20468 x666=20469 x667=20478 x668=20479 x669=20488 x670=20489
x671=20499 x672=20567 x673=20568 x674=20569 x675=20578 x676=20579 x677=20588 x678=20589 x679=20599 x680=20678
x681=20679 x682=20688 x683=20689 x684=20699 x685=20788 x686=20789 x687=20799 x688=20888 x689=20889 x690=20899
x691=20999 x692=22222 x693=22223 x694=22224 x695=22225 x696=22226 x697=22227 x698=22228 x699=22229 x700=22233
x701=22234 x702=22235 x703=22236 x704=22237 x705=22238 x706=22239 x707=22244 x708=22245 x709=22246 x710=22247
x711=22248 x712=22249 x713=22256 x714=22257 x715=22258 x716=22259 x717=22267 x718=22268 x719=22269 x720=22278
x721=22279 x722=22288 x723=22289 x724=22299 x725=22333 x726=22334 x727=22335 x728=22336 x729=22337 x730=22338
x731=22339 x732=22344 x733=22345 x734=22346 x735=22347 x736=22348 x737=22349 x738=22356 x739=22357 x740=22358
x741=22359 x742=22367 x743=22368 x744=22369 x745=22378 x746=22379 x747=22388 x748=22389 x749=22399 x750=22444
x751=22445 x752=22446 x753=22447 x754=22448 x755=22449 x756=22456 x757=22457 x758=22458 x759=22459 x760=22467
x761=22468 x762=22469 x763=22478 x764=22479 x765=22488 x766=22489 x767=22499 x768=22567 x769=22568 x770=22569
x771=22578 x772=22579 x773=22588 x774=22589 x775=22599 x776=22678 x777=22679 x778=22688 x779=22689 x780=22699
x781=22788 x782=22789 x783=22799 x784=22888 x785=22889 x786=22899 x787=22999 x788=23333 x789=23334 x790=23335
x791=23336 x792=23337 x793=23338 x794=23339 x795=23344 x796=23345 x797=23346 x798=23347 x799=23348 x800=23349
x801=23356 x802=23357 x803=23358 x804=23359 x805=23367 x806=23368 x807=23369 x808=23378 x809=23379 x810=23388
x811=23389 x812=23399 x813=23444 x814=23445 x815=23446 x816=23447 x817=23448 x818=23449 x819=23456 x820=23457
x821=23458 x822=23459 x823=23467 x824=23468 x825=23469 x826=23478 x827=23479 x828=23488 x829=23489 x830=23499
x831=23567 x832=23568 x833=23569 x834=23578 x835=23579 x836=23588 x837=23589 x838=23599 x839=23678 x840=23679
x841=23688 x842=23689 x843=23699 x844=23788 x845=23789 x846=23799 x847=23888 x848=23889 x849=23899 x850=23999
x851=24444 x852=24445 x853=24446 x854=24447 x855=24448 x856=24449 x857=24456 x858=24457 x859=24458 x860=24459
x861=24467 x862=24468 x863=24469 x864=24478 x865=24479 x866=24488 x867=24489 x868=24499 x869=24567 x870=24568
x871=24569 x872=24578 x873=24579 x874=24588 x875=24589 x876=24599 x877=24678 x878=24679 x879=24688 x880=24689
x881=24699 x882=24788 x883=24789 x884=24799 x885=24888 x886=24889 x887=24899 x888=24999 x889=25678 x890=25679
x891=25688 x892=25689 x893=25699 x894=25788 x895=25789 x896=25799 x897=25888 x898=25889 x899=25899 x900=25999
x901=26788 x902=26789 x903=26799 x904=26888 x905=26889 x906=26899 x907=26999 x908=27888 x909=27889 x910=27899
x911=27999 x912=28888 x913=28889 x914=28899 x915=28999 x916=29999 x917=30000 x918=30003 x919=30004 x920=30005
x921=30006 x922=30007 x923=30008 x924=30009 x925=30033 x926=30034 x927=30035 x928=30036 x929=30037 x930=30038
x931=30039 x932=30044 x933=30045 x934=30046 x935=30047 x936=30048 x937=30049 x938=30056 x939=30057 x940=30058
x941=30059 x942=30067 x943=30068 x944=30069 x945=30078 x946=30079 x947=30088 x948=30089 x949=30099 x950=30333
x951=30334 x952=30335 x953=30336 x954=30337 x955=30338 x956=30339 x957=30344 x958=30345 x959=30346 x960=30347
x961=30348 x962=30349 x963=30356 x964=30357 x965=30358 x966=30359 x967=30367 x968=30368 x969=30369 x970=30378
x971=30379 x972=30388 x973=30389 x974=30399 x975=30444 x976=30445 x977=30446 x978=30447 x979=30448 x980=30449
x981=30456 x982=30457 x983=30458 x984=30459 x985=30467 x986=30468 x987=30469 x988=30478 x989=30479 x990=30488
x991=30489 x992=30499 x993=30567 x994=30568 x995=30569 x996=30578 x997=30579 x998=30588 x999=30589 x1000=30599
x1001=30678 x1002=30679 x1003=30688 x1004=30689 x1005=30699 x1006=30788 x1007=30789 x1008=30799 x1009=30888 x1010=30889
x1011=30899 x1012=30999 x1013=33333 x1014=33334 x1015=33335 x1016=33336 x1017=33337 x1018=33338 x1019=33339 x1020=33344
x1021=33345 x1022=33346 x1023=33347 x1024=33348 x1025=33349 x1026=33356 x1027=33357 x1028=33358 x1029=33359 x1030=33367
x1031=33368 x1032=33369 x1033=33378 x1034=33379 x1035=33388 x1036=33389 x1037=33399 x1038=33444 x1039=33445 x1040=33446
x1041=33447 x1042=33448 x1043=33449 x1044=33456 x1045=33457 x1046=33458 x1047=33459 x1048=33467 x1049=33468 x1050=33469
x1051=33478 x1052=33479 x1053=33488 x1054=33489 x1055=33499 x1056=33567 x1057=33568 x1058=33569 x1059=33578 x1060=33579
x1061=33588 x1062=33589 x1063=33599 x1064=33678 x1065=33679 x1066=33688 x1067=33689 x1068=33699 x1069=33788 x1070=33789
x1071=33799 x1072=33888 x1073=33889 x1074=33899 x1075=33999 x1076=34444 x1077=34445 x1078=34446 x1079=34447 x1080=34448
x1081=34449 x1082=34456 x1083=34457 x1084=34458 x1085=34459 x1086=34467 x1087=34468 x1088=34469 x1089=34478 x1090=34479
x1091=34488 x1092=34489 x1093=34499 x1094=34567 x1095=34568 x1096=34569 x1097=34578 x1098=34579 x1099=34588 x1100=34589
x1101=34599 x1102=34678 x1103=34679 x1104=34688 x1105=34689 x1106=34699 x1107=34788 x1108=34789 x1109=34799 x1110=34888
x1111=34889 x1112=34899 x1113=34999 x1114=35678 x1115=35679 x1116=35688 x1117=35689 x1118=35699 x1119=35788 x1120=35789
x1121=35799 x1122=35888 x1123=35889 x1124=35899 x1125=35999 x1126=36788 x1127=36789 x1128=36799 x1129=36888 x1130=36889
x1131=36899 x1132=36999 x1133=37888 x1134=37889 x1135=37899 x1136=37999 x1137=38888 x1138=38889 x1139=38899 x1140=38999
x1141=39999 x1142=40000 x1143=40004 x1144=40005 x1145=40006 x1146=40007 x1147=40008 x1148=40009 x1149=40044 x1150=40045
x1151=40046 x1152=40047 x1153=40048 x1154=40049 x1155=40056 x1156=40057 x1157=40058 x1158=40059 x1159=40067 x1160=40068
x1161=40069 x1162=40078 x1163=40079 x1164=40088 x1165=40089 x1166=40099 x1167=40444 x1168=40445 x1169=40446 x1170=40447
x1171=40448 x1172=40449 x1173=40456 x1174=40457 x1175=40458 x1176=40459 x1177=40467 x1178=40468 x1179=40469 x1180=40478
x1181=40479 x1182=40488 x1183=40489 x1184=40499 x1185=40567 x1186=40568 x1187=40569 x1188=40578 x1189=40579 x1190=40588
x1191=40589 x1192=40599 x1193=40678 x1194=40679 x1195=40688 x1196=40689 x1197=40699 x1198=40788 x1199=40789 x1200=40799
x1201=40888 x1202=40889 x1203=40899 x1204=40999 x1205=44444 x1206=44445 x1207=44446 x1208=44447 x1209=44448 x1210=44449
x1211=44456 x1212=44457 x1213=44458 x1214=44459 x1215=44467 x1216=44468 x1217=44469 x1218=44478 x1219=44479 x1220=44488
x1221=44489 x1222=44499 x1223=44567 x1224=44568 x1225=44569 x1226=44578 x1227=44579 x1228=44588 x1229=44589 x1230=44599
x1231=44678 x1232=44679 x1233=44688 x1234=44689 x1235=44699 x1236=44788 x1237=44789 x1238=44799 x1239=44888 x1240=44889
x1241=44899 x1242=44999 x1243=45678 x1244=45679 x1245=45688 x1246=45689 x1247=45699 x1248=45788 x1249=45789 x1250=45799
x1251=45888 x1252=45889 x1253=45899 x1254=45999 x1255=46788 x1256=46789 x1257=46799 x1258=46888 x1259=46889 x1260=46899
x1261=46999 x1262=47888 x1263=47889 x1264=47899 x1265=47999 x1266=48888 x1267=48889 x1268=48899 x1269=48999 x1270=49999
x1271=50000 x1272=50006 x1273=50007 x1274=50008 x1275=50009 x1276=50067 x1277=50068 x1278=50069 x1279=50078 x1280=50079
x1281=50088 x1282=50089 x1283=50099 x1284=50678 x1285=50679 x1286=50688 x1287=50689 x1288=50699 x1289=50788 x1290=50789
x1291=50799 x1292=50888 x1293=50889 x1294=50899 x1295=50999 x1296=56788 x1297=56789 x1298=56799 x1299=56888 x1300=56889
x1301=56899 x1302=56999 x1303=57888 x1304=57889 x1305=57899 x1306=57999 x1307=58888 x1308=58889 x1309=58899 x1310=58999
x1311=59999 x1312=60000 x1313=60007 x1314=60008 x1315=60009 x1316=60078 x1317=60079 x1318=60088 x1319=60089 x1320=60099
x1321=60788 x1322=60789 x1323=60799 x1324=60888 x1325=60889 x1326=60899 x1327=60999 x1328=67888 x1329=67889 x1330=67899
x1331=67999 x1332=68888 x1333=68889 x1334=68899 x1335=68999 x1336=69999 x1337=70000 x1338=70008 x1339=70009 x1340=70088
x1341=70089 x1342=70099 x1343=70888 x1344=70889 x1345=70899 x1346=70999 x1347=78888 x1348=78889 x1349=78899 x1350=78999
x1351=79999 x1352=80000 x1353=80008 x1354=80009 x1355=80088 x1356=80089 x1357=80099 x1358=80888 x1359=80889 x1360=80899
x1361=80999 x1362=88888 x1363=88889 x1364=88899 x1365=88999 x1366=89999 x1367=90000 x1368=90009 x1369=90099 x1370=90999
x1371=99999




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