Similar to Different (or) A+B+C=N

Q. Find the number of ways of distributing 7 identical balls into three different boxes so that no box is empty and each box being large enough to accomodate all balls.

1. 15
2. $7^3$
3. $3^7$
4. $\frac{7!}{3!}$

Q. There are 3 pots and 4 coins. All these coins are to be distributed into these pots where any pot can contain any number of coins.

In how many ways all these coins can be distributed if out of 4 coins 2 coins are identical and all pots are different?

1. 27
2. 54
3. 45
4. None of these

Q. There are 3 pots and 4 coins. All these coins are to be distributed into these pots where any pot can contain any number of coins.

In how many ways all these coins can be distributed such that no pot is empty if all coins are identical but all pots are different?

1. 3
2. 9
3. 6
4. 27

Q. There are 3 pots and 4 coins. All these coins are to be distributed into these pots where any pot can contain any number of coins.

In how many ways all these coins can be distributed if all coins are identical but all pots are different?

1. 17
2. 81
3. 15
4. 16

Q. There are 5 different boxes and 7 different balls. All the 7 balls are to be distributed in the 5 boxes placed in a row so that any box can receive any number of balls.

Suppose all the balls are identical, then in how many ways can all these balls be distributed into these boxes?

1. 220
2. 330
3. 110
4. 440

Q. There are 5 different caps $c_1,c_2,c_3,c_{4}and{c}_5$ and 5 different boxes $B_1,B_2,B_3,B_{4}and{B}_5$. The capacity of each box is sufficient to accomodate all the 5 caps.

If all the caps are identical, in how many ways can the caps be arranged in the different boxes such that no box is empty?

1. 2
2. 6
3. 8
4. 1

Q. In how many different ways can 6 identical balls be distributed to 4 different boxes, when each box can have any number of balls?

1. 12
2. 18
3. 84
4. 88

Q. In how many ways can 8 identical apples be divided among 3 sisters?

1. 25
2. 65
3. 45
4. 24