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 different but all pots are identical?

• A. 14
• B. 21
• C. 27
• D. none of these

Answer 1

The correct option is A 14

Since pots are identical then there will be 4 cases (4, 0, 0), (3, 1, 0), (2, 2, 0) and (2, 1, 1) but since all coins are different hence the selection of coins matters.
Therefore for the first case, number of selections $={}^4{C}_4=1$
For the second case, number of selections ${=}^4{C}_3{\times }^1{C}_1=4$
For the third case, number of selections $=\frac{{}^4{C}_2{\times }^2{C}_2}{2!}=3$
For the fourth case, number of selections
$=\frac{{}^4{C}_2{\times }^2{C}_1{\times }^1{C}_1}{2!}=6$
Hence the total number of distributions = 1 + 4 + 3 + 6 = 14