1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Permutations and Combinations

Solution:

We know that the number of ways of distributing n identical items among r persons, when each one of them receives at least one item is ${^{n-1}C_{r-1}}$
$\therefore $ The required number of ways
$= ^{8-1}C_{3-1}= ^{7}C_{2} = \frac{7!}{2!5!}= \frac{7 \times6}{2 \times1} = 21 $