Combinations 80637

If the number of elements decreases by 4, the number of combinations of the second class from these elements decreases three times. How many elements are there?

Correct answer:

n =  10

Step-by-step explanation:

C2(6)=(26)=2!(62)!6!=2165=15 (2n)/3 = (2n4) 2 (n2)!n! = 3  2 (n6)!(n4)! (n2)!n(n1)(n2)! = 3  (n6)!(n4)(n5)(n6)!  n(n1)=3 (n4) (n5)  n(n1)=3 (n4) (n5) 2n2+26n60=0 2n226n+60=0 2 ...  prime number 26=213 60=2235 GCD(2,26,60)=2  n213n+30=0  a=1;b=13;c=30 D=b24ac=1324130=49 D>0  n1,2=2ab±D=213±49 n1,2=213±7 n1,2=6.5±3.5 n1=10 n2=3  n>3 n=n1=10   Verifying Solution:  c1=(2n)=45 C2(10)=(210)=2!(102)!10!=21109=45  c2=(2n4)=(2104)=15 3 c2=c1

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