Question

There are 3 pots and 4 coins. All these coins are to be distributed among 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 and two pots are also identical?

• A. 1
• B. 10
• C. 9
• D. 11

Answer 1

The correct option is C 9

The possible arrangements are as follows.
(4, 0, 0) $\to$ can be done in 2 ways
i.e., 4 balls can be put either one of the two identical pots or can be put in different pot.
(3, 1, 0) $\to$ can be done in 3 ways either distinct pot can be filled up with 3 balls, or 1 ball or remained empty.
(2, 2, 0) $\to$ can be done in 2 ways
either distinct pot can be filled by 2 balls or remained empty.
(2, 1, 1) $\to$ can be done in 2 ways
either distinct pot can be filled up with 1 ball or 2 ball.
Hence, the required number of ways $=2+3+2+2=9$