The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
JEE · Math · previous-year question
- A.$${}^8{C_3}$$
- B.21correct
- C.$${3^8}$$
- D.5
Answer
B. 21
Explanation
To distribute n objects among p people where everyone should get atleast one object, then number of ways to distribute those n objects = $${}^{n - 1}{C_{p - 1}}$$ For this question, n = 8 and p = 3 $$ \therefore $$ Number of ways = $${}^{8 - 1}{C_{3 - 1}}$$ = $${}^7{C_2}$$ = 21
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