For each positive integer n, let `A_n=max{(C(n,r) 0 le r le n}` then the number of elements n in {1,2...20} for `1.9 le (A_n)/(A_(n-1)) le 2` is

If n and r are integers such that 1 le r le n then n. C (n-1,r-1)=

IF n and r are positive inegers such that r le n then ""^(n) C_(r) + ""^(n)C_(r-1) =

Let n_1 le n_2< n_3 < n_4< n_5 be positive integers such that n_1+n_2+n_3+n_4+n_5=20. then the number of such distinct arrangements n_1, n_2, n_3, n_4, n_5 is

Let P(n) be the statement: C_(r)len! for 1le r le n Is P(3) true ?

If n and r are positive integers such that. 2 le r le n , show that overset(n) C_r+2 overset(n) C_{r-1}+overset(n) C_(r-2)=overset(n+2) C_r

IF n is an integer with 0 le n le 11 then the minimum value of n !(11-n)! is attained when a value of n=

Probability of getting positive integral roots of the equation x^(2)-n=0 for the integer n, 1 le n le 40 is