Permutations with repetitions

How many times the input of 1.2.2.3.3.3.4 can be permutated into 4 digits, 3 digits and 2 digits without repetition?
Ex:
4 digits = 1223, 2213, 3122, 2313, 4321. . etc
3 digits = 122.212.213.432. . etc
2 digits = 12, 21, 31, 23

I have tried permutation formula and it failed.

Correct result:

n4 =  115
n3 =  43
n2 =  14

Solution:

a1=1223;a2=1224;a3=1232;a4=1233;a5=1234;a6=1242;a7=1243;a8=1322;a9=1323;a10=1324;a11=1332;a12=1333;a13=1334;a14=1342;a15=1343;a16=1422;a17=1423;a18=1432;a19=1433;a20=2123;a21=2124;a22=2132;a23=2133;a24=2134;a25=2142;a26=2143;a27=2213;a28=2214;a29=2231;a30=2233;a31=2234;a32=2241;a33=2243;a34=2312;a35=2313;a36=2314;a37=2321;a38=2323;a39=2324;a40=2331;a41=2332;a42=2333;a43=2334;a44=2341;a45=2342;a46=2343;a47=2412;a48=2413;a49=2421;a50=2423;a51=2431;a52=2432;a53=2433;a54=3122;a55=3123;a56=3124;a57=3132;a58=3133;a59=3134;a60=3142;a61=3143;a62=3212;a63=3213;a64=3214;a65=3221;a66=3223;a67=3224;a68=3231;a69=3232;a70=3233;a71=3234;a72=3241;a73=3242;a74=3243;a75=3312;a76=3313;a77=3314;a78=3321;a79=3322;a80=3323;a81=3324;a82=3331;a83=3332;a84=3333;a85=3334;a86=3341;a87=3342;a88=3343;a89=3412;a90=3413;a91=3421;a92=3422;a93=3423;a94=3431;a95=3432;a96=3433;a97=4122;a98=4123;a99=4132;a100=4133;a101=4212;a102=4213;a103=4221;a104=4223;a105=4231;a106=4232;a107=4233;a108=4312;a109=4313;a110=4321;a111=4322;a112=4323;a113=4331;a114=4332;a115=4333;  n4=115
b1=122;b2=123;b3=124;b4=132;b5=133;b6=134;b7=142;b8=143;b9=212;b10=213;b11=214;b12=221;b13=223;b14=224;b15=231;b16=232;b17=233;b18=234;b19=241;b20=242;b21=243;b22=312;b23=313;b24=314;b25=321;b26=322;b27=323;b28=324;b29=331;b30=332;b31=333;b32=334;b33=341;b34=342;b35=343;b36=412;b37=413;b38=421;b39=422;b40=423;b41=431;b42=432;b43=433;  n3=43
c1=12;c2=13;c3=14;c4=21;c5=22;c6=23;c7=24;c8=31;c9=32;c10=33;c11=34;c12=41;c13=42;c14=43;  n2=14



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