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JEE Main · 2004 · 24 Apr 2004 · Offline · Permutations and Combinations

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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
  1. (A)5
  2. (B)
  3. (C)
  4. (D)21✓ Correct

Answer: (D)

Solution

The requirement that no box stays empty is handled neatly by first dropping one ball into each of the three boxes; that leaves identical balls to spread freely among the boxes. The number of ways of doing this is the stars-and-bars count .

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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