Permutations And Combinations

Question
CBSEENMA11015665

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

  • 5

  • 8C3
  • 38

  • 21

Solution

D.

21

The required number of ways
space equals space to the power of 8 minus 1 end exponent straight C subscript 3 minus 1 end subscript
space equals space to the power of 7 straight C subscript 2 space equals space fraction numerator 7 factorial over denominator 2 factorial 5 factorial end fraction
space equals space to the power of 7 straight C subscript 2 space equals space fraction numerator 7 space factorial over denominator 2 factorial space 5 factorial end fraction
space equals space fraction numerator 7.6 over denominator 2.1 end fraction space equals space 21

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