There are two bags can each of which contains `n` balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is `^2n C_n-1.`

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is^(2n)C_n-1.

Eight questions are given , each question has an alternative Prove that the number of ways in which a student can select one or more Questions is (2^(8)-1) .

A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select at least one book is 63, find the value of n.

There are p copies each of n different books. Find the number of ways in which a nonempty selection can be made from them.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Given that n is the odd the number of ways in which three numbers in A.P. can be selected from {1,2,3,4….,n} is

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that atleast one ball is separated from the balls of the same color.

There are four balls of different colours and four boxes of colours same as those of the balls. Find the number of way in which the balls ,one in each box,of its own colour.

There are 5 different colour balls and 5 boxes of colours same as those of the balls. The number of ways in which one can place the balls into the boxes, one each in a box, so that no ball goes to a box of its own colour is

Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to a. .^9C_5 b. .^10 C_5 c. .^6C_5 d. .^10 C_6