Question

K=n(n-1)(n-2)(n-3)........3*2*1 .find out the number of possible values of K for which K is not divisible by n+1 where n is less than or equal to 100.

Answer 1

hai friend,
here n(n-1)(n-2)(n-3)........3*2*1 =n!
so k=n!
we know k<=100
if n=1,k=1
n=2,k=2
n=3,k=6
n=4,k=24
n=5,k>100
we also know k not divisible by (n+1)

checking the above
n=1,k=1, 1/(1+1) not divisible
n=2,k=2, 2/3 not divisible
n=3,k=6,6/4 not divisible
n=4,k=24,24/5 not divisible

therefore Number of possible values of k is 4

hope helped:-)