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)`

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

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

Prove that n! (n+2) = n! +(n+1)! .

Prove that ((n + 1)/(2))^(n) gt n!

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

Prove that [(n+1)//2]^n >(n !)dot

Prove that the no. of permutations of n different objects taken r at a time in which two specified objects always occur together 2!(r-1) (n-2)P_(r-2)

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

Prove that: \ ^(2n)C_n=(2^n[1. 3. 5 (2n-1)])/(n !)

Given that n is odd, number of ways in which three numbers in AP can be selected from 1, 2, 3,……., n, is