A box contains 5 different res and 6, different whit balls. In how many ways can 6 balls be selected so that there are at least two balls off each color?

A box contains 2 white balls, 3 black balls & 4 red balls. In how many ways can three balls be drawn from the box if atleast one black ball is to be included in draw (the balls of the same colour are different).

The Indian cricket eleven is to be selected out of 15 players. 6 of them bowlers and 9 of them batsman. In how many ways the team can be selected so that the team contains at least 3 bowlers.

In how many ways can 12 balls be divided between 2 boys, one receiving 5 and the other 7 balls ?

A box contains 12 lamps of which 5 are defective . In how many ways can a sample of 6 be selected at random from the box so as to include at most 3 defective lamps ?

A box contains 12 red and 6 white balls. Balls are drawn from the bag one at a time without replacement. If in 6 draws, there are at least 4 white balls, find the probability the exactly one white ball is drawn in the next two draws. (Binomial coefficients can be left as such.)

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

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 committee of 5 is to be formed from six ladies and four gentlemen . In how many ways this can be done so that the committee contains at least two ladies,

In how many ways 5 different balls can be distributed into 3 boxes so that no box remains empty ?

For an examination a candidate has to select 7 subjects from 3 different groups A,B,C which contain 4,5,6 subjects respectively in how many different ways can a candidate make his selection if he has to select at least 2 subjects from each group?