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Question

Ten distinct balls are put into nine indistinguishable boxes so that no box is empty. The number of ways of placing these balls is?

2017-02-01 19:25:48

vyom
1 Answer

**Solution 1**

Select any two balls and place in any of the box. $10\text{C}2$ ways. Remaining eight balls can be placed in the remaining eight boxes like one ball in each box.

Required number of ways $=10\text{C}2=45$

**Solution 2**

See formula 11

Required count $=S(10,9)=\dbinom{10}{2}=45$