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

if n objects are arranged 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

Find the number of ways of disturbing n identicalobjects among n persons if at least n-3 persons get none of these objects.

Let f(n ,k) denote the number of ways in which k identical balls can be colored with n colors so that there is at least one ball of each color. Then f(n ,2n) must be equal to a. ""^(2n) C_n b. ""^(2n-1)C_(n+1) c. ""^(2n-1)C_n d. none of these

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n

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

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

n different things are arranged around a circle. In how many ways can 3 object be selected when no two of the selected objects are consecutive.

If ""^n C_3+ ""^n C_4 > ""^(n+1)C_3 , then a. n >6 b. n >7 c. n 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