Question

A restaurant lunch special allows the customer to choose four vegetables from the following group.peas caulfower squash angula carrots spinachHow many outcomes are possible if the customer chooses four different vegetables?The customer can choose tour vegetablesdifferent ways(Simplify your answer)w

Answer 1

ANSWER :

15 different ways

EXPLANATION :

Recall the combination formula :

$_nC_r=\frac{n!}{(n-r)!r!}$

where r is taken from n items.

From the problem, we have 6 vegetables to choose from. So n = 6

And a customer is allowed to choose four vegetables. So r = 4

Using the formula above :

$\begin{gathered} _6C_4=\frac{6!}{(6-4)!4!}=\frac{6!}{2!\times4!} \\ \\ =\frac{6\times5\times4!}{2!\times4!} \\ \\ =\frac{6\times5}{2} \\ \\ =3\times5 \\ \\ =15 \end{gathered}$