A probability problem by Fares Salem

Probability Level 2

In a local store there are 8 different shirts, 7 different pairs of pants, and 3 different pairs of shorts in your size. How many different outfits can you buy?

Note: An outfit consists of a shirt, along with a pair of pants or a pair of shorts.


The answer is 80.

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Fares Salem by Fares Salem , 22, Egypt

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3 solutions

Vinayak Verma
Oct 20, 2015

A person can choose either a pair of pants or a pair of shorts. So, applying the Rule of Sum ,

No. of choices = 3 + 7 = 10 3 +7 = 10

To go with these 10 choices, one can choose from 8 shirts. So, applying the Rule of Product ,

Total no. of choices = 8 ∗ 10 = 80 8 * 10 =\boxed{80}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good use of the rule of sum and rule of product :)

Fares Salem
Oct 17, 2014

a shirt and a pair of pants OR a shirt and a pair of shorts is the outfit :)

so the answer is as the following ;

8 × 7 + 8 × 3 = 80

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Cool problem as ever!

Swapnil Das - 5 years, 8 months ago
Ariella Lee
Dec 8, 2015

Two ways to make an outfit:

1) Shirt & Pants: 8 × 7 = 56 8\times7=56

2) Shirt & Shorts 8 × 3 = 24 8\times3=24

Since these are the only two ways to make an outfit, every outfit is counted at least once. There are no overlaps (no outfit is overcounted), and so every outfit has been counted exactly once.

Total: 56 + 24 = 80 56+24=\boxed{80}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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