Question

A restaurant has 5 side dishes, 6 main dishes and 2 desserts. A student chooses one side dish and one dessert. How many different meals could she make?

Answer 1

SOLUTION

From the 5 side dishes, the student choose 1 side dish and can use this to make a meal in 5 ways, considering the 5 side dishes.

From the 2 desserts, she can choose 1 dessert and make meal in 2 ways, considering the 2 desserts.

In combination, we have to multiply. So the student can make meals in

$5ways\times2ways=10\text{ways }$

Hence the answer is 10 different meals

We can also say selecting 1 side dish from 5 side dishes and

selecting 1 dessert from 2 desserts. This becomes

$\begin{gathered} ^5C_1\times^2C_1 \\ =\frac{5!}{(5-1)!1!}\times\frac{2!}{(2-1)!1!} \\ =\frac{5\times4!}{4!}\times\frac{2\times1!}{1!} \\ =5\times2 \\ =10\text{ ways} \end{gathered}$

Hence 10 different meals