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School uniform brainteaser

By David Shaw, 23 February 2022

Difficulty: Tricky

Keira is getting ready for school:

• She has 3 different shirts – one black, one white and one red.
• She has 3 different pairs of pants – one black, one white and one red.
• She has 3 different pairs of shoes – one black, one white and one red.

Keira is going to wear one shirt, one pair of pants and one pair of shoes. She also wants to wear one black item, one white item and one red item. How many ways can she get dressed?

Scroll down or click for a hint, or the answer!

 

Brainteaser hint

If Keira first chooses a black item, how many black options does she have? How many white choices does that leave? Once the white item is chosen, how many red options are left?

Brainteaser answer

First, Keira chooses a black item – there are 3 options to choose from. Then she chooses a white item – there are only 2 items to choose from, because she’s already wearing one piece of clothing. Then she chooses a red item. There’s only one item of clothing she hasn’t put on yet, so she doesn’t get a choice.

So, Keira gets a choice with 3 options and one with 2 options. That means 3 x 2 = 6 different outfits:

• Black shirt, white pants, red shoes
• Black shirt, white shoes, red pants
• Black pants, white shirt, red shoes
• Black pants, white shoes, red shirt
• Black shoes, white shirt, red pants
• Black shoes, white pants, red shirt.

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