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.`

A bag has contains 23 balls in which 7 are identical . Then number of ways of selecting 12 balls from bag.

A bag contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is 2/5, find the number of red balls in the bag.

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.

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.

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.

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.

There are 4 red, 3 black and 5 white balls in a bag. Find the number of ways of selecting three balls, if at least one black ball is there.

There are 4 white, 3 black and 3 red balls in a bag. Find the number of ways of selecting three balls, if at least one black ball is there.

Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done, if atleast 2 are red, is.

There are two bags. One bag contains six green and three red balls. The second bag contains five green and four red balls. One ball is transferred from the first bag to the second bag. Then one ball is drawn from the second bag. Find the probability that it is a red ball.