Question

A student has three mangos, two papayas, and two kiwi fruits. If the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed?

Short answer

Therefore, there are\(210\)ways to consume the fruits in the given order.

Step-by-step solution

Step 1: Assumptions and substitution

We assume that all the fruits are to be eaten; in other words, this process ends after seven days.

This is a permutation problem since the order in which the fruits are consumed matters.

Step 2: Further simplification

This is a permutation problem since the order in which the fruits are consumed matters.(indeed, there is nothing else that matters here).

Theorem three of the book applies with

\(n = 7\)

\(\begin{array}{l}{n_1} = 7\\{n_2} = 2\\{n_3} = 2\end{array}\)

Therefore we get the answer as

\(\begin{array}{l}\frac{{n!}}{{{n_1}!{n_2}!......{n_k}!}} = \frac{{7!}}{{3!2!2!}}\\ = 210\end{array}\)

Therefore, there are\(210\)ways to consume the fruits in the given order.