Question

In this question, there are 5 identical apples and 6 identical oranges to be distributed.

(a) How many ways are there to distribute the fruit among 4 children? 1

(b) How many ways are there to do this if each child needs to receive at least one orange and not all of the fruit is required to be handed out?

(c) How many ways are there to distribute the fruit among 3 children such that no child receives two different types of fruit?2

(d) How many ways are there to lay the fruit in 3 piles? The piles must not be empty but it doesn’t matter which pile is which.

(e) If one of the 3-pile arrangements from part (d) is chosen uniformly at random, what is the probability that each pile consists of only one type of fruit?

1It is allowed for some child or children to receive nothing.

2Again, it is allowed for some child or children to receive nothing.

Answer 1