### Brain Teasers

# Mix 'n Match

An older sister bragged that she had 30 different new outfits to wear to school.

Her younger brother said, "That's not true. You have 3 pairs of jeans, 5 shirts, and 2 pairs of shoes. There's no way that makes 30 different outfits. You only have 10 outfits."

Who is correct and why?

Her younger brother said, "That's not true. You have 3 pairs of jeans, 5 shirts, and 2 pairs of shoes. There's no way that makes 30 different outfits. You only have 10 outfits."

Who is correct and why?

### Answer

The older sister is correct. There are 30 different ways to mix and match the pants, shirts, and shoes.One pair of jeans goes with 5 shirts, so there are (3 x 5) or 15 jeans/shirts combinations. Each of these combinations can be worn with either of two pairs of shoes, which makes (15 x 2) or 30 different outfits.

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