Question

In how many ways can 10 identical objects be put in 8 distinct boxes in such that no box is empty?

• A. 9
• B. 36
• C. 45
• D. 10

Hint:

In "stars and bars" problems, use the formula \(\binom{n-1}{k-1}\) to find the number of ways to distribute \(n\) identical objects into \(k\) boxes.

Answer 1

The Correct Option is B

This is a classic example of the "stars and bars" problem where the formula to calculate the number of ways to distribute \(n\) identical objects into \(k\) distinct boxes is given by: \[ \binom{n-1}{k-1} \] In this case, \(n = 10\) and \(k = 8\), so the number of ways is: \[ \binom{10-1}{8-1} = \binom{9}{7} = 36 \]