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 n(gt2) distinct objects in a line so that two particulars objects are never together is

Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 2^(2n-1)+((2n) !)/(2(n !)^2)

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

If the number of ways of selecting r balls with replcement out of n balls numbered 1,2,3……,100 such that the largest number selected is 10 is 271, then r= (A) 4 (B) 5 (C) 3 (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

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

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these