Question

Shirts and Ties: A man has 5 shirts and 3 ties. How many

different shirt and tie arrangements can he wear?

Short answer

There are 15 different shirt and tie arrangements he can

wear.

Step-by-step solution

 Step 1. Given information

$$\begin{gathered} \mathrm{Let}\mathrm{number}\mathrm{of}\mathrm{Shirts}\mathrm{be}\mathrm{p}\mathrm{and}\mathrm{number}\mathrm{of}\mathrm{Ties}\mathrm{be}\mathrm{q}: \\ \mathrm{p}=5 \\ \mathrm{q}=3 \end{gathered}$$

 Step 2. Calculation

$$\begin{gathered} \mathrm{Different}\mathrm{shirt}\mathrm{and}\mathrm{tie}\mathrm{arrangements}\mathrm{he}\mathrm{can}\mathrm{wear}\mathrm{is}(\mathrm{p}·\mathrm{q}) \\ \mathrm{p}·\mathrm{q}=5\times 3 \\ \mathrm{p}·\mathrm{q}=15 \end{gathered}$$