The number of ways in which we can distribute `m n` students equally among `m` sections is given by a. `((m n !))/(n !)` b. `((m n)!)/((n !)^m)` c. `((m n)!)/(m ! n !)` d. `(m n)^m`

Find the number of ways in which n different prizes can be distributed among m(< n) persons if each is entitled to receive at most n-1 prizes.

2m white counters and 2n red counters are arranged in a straight line with (m+n) counters on each side of central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is (A) .^(m+n)C_m (B) .^(2m+2n)C_(2m) (C) 1/2 ((m+n)!)/(m! n!) (D) None of these

A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local maximum value of the function is (m ,n in N), 1 (b) m^nn^m (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(m+n))

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

The number of ways of arranging m positive and n(lt m+1) negative signs in a row so that no two are together is a)^m+1p_n b ^n+1p_m c)^m+1C_n d)^n+1c_m

The number of ordered pairs (m,n) where m , n in {1,2,3,…,50} , such that 6^(m)+9^(n) is a multiple of 5 is

If sum of m terms is n and sum of n terms is m, then show that the sum of (m + n) terms is -(m + n).