The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is - Mathematics MCQ AIEEE 2004 2004 | ExamTest.live | ExamTest.live

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

A $5$
B $^{8} C_{3}$
C $3^{8}$
D $21$

Solution & Step-by-step Explanation

This is a problem of distributing n identical items into r distinct bins such that each bin receives at least one item. The formula for this is^{n - 1} C_{r - 1} . Here, n = 8 (balls) and r = 3 (boxes). Number of ways =^{8 - 1} C_{3 - 1} =^{7} C_{2} .^{7} C_{2} = \frac{7 \times 6}{2 \times 1} = 21 .

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

A

5

B

^{8} C_{3}

C

3^{8}

D

21

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