If `n` objects are arrange in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is a. `"^(n-2)C_3` b. `"^(n-3)C_2` c. `"^(n-3)C_3` d. none of these

Which of the following is not the number of ways of selecting n objects from 2n objects of which n objects are identical

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

n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. sum_(k=1)^(n-1)k b. n(n-1) c. n^2 d. none of these

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is (a). .^n C_3xx2^n (b). .^n C_2xx3^(n-2) (c). 3^(n-1) (d). none of these

The number of possible outcomes in a throw of n ordinary dice in which at least one of the die shows and odd number is a. 6^n-1 b. 3^n-1 c. 6^n-3^n d. none of these

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

If ""^(2n)C_(3) : ""^(n) C_(3)= 11 : 1 then n is

The number of triangles that can be formed with 10 points as vertices n of them being collinear, is 110. Then n is a. 3 b. 4 c. 5 d. 6

The total number of ways in which 2n persons can be divided into n couples is a. (2n !)/(n ! n !) b. (2n !)/((2!)^3) c. (2n !)/(n !(2!)^n) d. none of these

The total number of ways in which n^2 number of identical balls can be put in n numbered boxes (1,2,3,.......... n) such that ith box contains at least i number of balls is a. .^(n^2)C_(n-1) b. .^(n^2-1)C_(n-1) c. .^((n^2+n-2)/2)C_(n-1) d. none of these