Question

In how many ways can 3 peaches, 2 tangerines, 4 mangos, and 1 apple be given to 10 children if each child receives exactly 1 piece of fruit?

25,200
12,600
24
288

Answer 1

The number of permutations of 10 different things is 10!. The number of permutations of the 3 peaches is 3! and each of these permutations does not change the distribution of the fruit. There are also 2! permutations of the tangerines and 4! permutations of the mangoes which do not change the distribution of the fruit. Therefore the number of ways the fruit can be distributed is given by:
\[\large \frac{10!}{3! \times2! \times4!}=you\ can\ calculate\]

Answer 2

Thank you for the detailed response!

Answer 3

You're welcome :)