The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ______.

Name: The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ______.
Uploaded: 2026-05-07T11:32:19.051884+05:30
Duration: 1 min 11 s
Description: The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ______.

Correct Answer: 171

Solution

We will use this formula and it is used whenever we are solving these types of questions.

$$^{n-1}C_{r-1}=\frac{\left(n-1\right)!}{\left(n-r\right)!\left(r-1\right)!}=\frac{\left(20-1\right)!}{\left(17\right)!\left(3-1\right)!}=\frac{19\times\ 18}{2\times\ 1}=171$$