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Combination of Atleast One Thing from n Things When All Are Not Different

The number of...

Question

The number of ways of distributing eight identical balls in three distinct boxes so that none of the boxes is empty is

A

5

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B

^{8} C_{3}

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C

3^{8}

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D

21

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Solution

The correct option is D 21
The required number of ways $=^{8 - 1} C_{3 - 1} =^{7} C_{2} = \frac{7!}{2! 5!} = \frac{7 \times 6}{2 \times 1} = 21$

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