In how many ways can `2t+1` identical balls be placed in three distinct boxes so that any two boxes together will contain more balls than the third?

Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

In how many ways 10 different balls can be put in 2 difference boxes ?

In how many ways can we get a sum greater than 17 by throwing six distinct dice.

In how many ways 14 identical toys be distributed among three boys so that each one gets atleast one toy and no two boys get equal no of toys ?

In how many Ways 6 different balls can be distributed among 4 boxes.

In how many ways can 3 ladies and 3 gentlemen be seated around a round table so that any two and only two of the ladies sit together?

In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together?

In how many ways can the letters of the word 'GLOOMY' be arranged so that the two O's should not be together?

Number of ways in which 6 distinct objects can be kept into two identical boxes so that no box remains empty is

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is : (1) (55)/3(2/3)^(11) (2) 55(2/3)^(10) (3) 220(1/3)^(12) (4) 22(1/3)^(11)