Home
Class 12
MATHS
In how many ways can 2t+1 identical ball...

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?

Text Solution

Verified by Experts

The total number of ways to place the balls disregarding the constrains is `""^(2t+1+3-1)C_(3-1)= ""^(2t+3)C_(2)`.
The total number of ways to place the balls so that the first box will have balls than the other two is
`""^(t+3-1)C_(3-1)=""^(t+2)C_(2)`.
[We place t+1 balls in the first box and then divide the rest of t balls in the three boxes arbitrarily.]
Promotional Banner

Similar Questions

Explore conceptually related problems

How many ways n distinct objects be placed in 2 different boxes so that no box remains empty?

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

In how many ways can 10 boys and 5 girls be seated in a round table so that two girls never be seated together ?

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 :

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-

In how many ways can 6 boys and 4 girls be seated in a round table so that two girls never be seated together.

In how many ways can six students be seated in a line so that two particular students do not sit together?

In how many ways can 12 examination papers be arranged so that the best and the worst papers may never come together ?

In how many ways can a person post 5 letters in 4 letters boxes ?

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