Outfits on World Tour

Probability Level 1

Suzy is going on an 80-day tour around the world. She has packed 7 tops, 5 bottoms, and 3 footwear. Being social-media conscious, she wants to post a selfie everyday to showcase her different outfits. To stay fresh, she does not want to wear the same outfit twice.

Does she have enough outfits to last 80 days?

Yes No

Chung Kevin by Chung Kevin , 45, Australia

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4 solutions

Jesse Nieminen
Jan 18, 2017

Suzy has 7 7 tops, 5 5 bottoms and 3 3 footwear.

By the Rule of Product , she has 7 × 5 × 3 = 105 ≥ 80 7 \times 5 \times 3 = 105 \geq 80 different outfits.

Hence, she does have enough outfits to last 80 80 days and the answer is Yes \boxed{\text{Yes}} .

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Jolon Behrent
Jan 16, 2017

Each day, Suzy has the choice of 7 different pairs of pants. For each pair of pants there are 5 different shirts she can wear. Meaning there are a total of 35 different pants and shirts combinations. Then there are 3 pairs of shoes for the 35 combinations leaving a total of 105 different outfits.

TL;DR: Just multiply everything

4 Helpful 0 Interesting 0 Brilliant 0 Confused

I agree But 3 pairs of shoes is simply just that.. 3. Even if she mixmatched the shoes it would not be a

TRULY New / different / outfit for EVERY day.

Right?? 🤐

Kyle Gawthrop - 4 years, 4 months ago
Khushi Mehta
Jan 18, 2017

5C1×7C1×3C1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Some points in this question are not clarified:

Are the 7 tops all different?

Are the 5 bottoms all different?

Are the 3 footwear all different?

If they are all different, then the answer is yes...

(Moreover, suppose that the 3 footwear are shoes. Is Suzy allowed to wear a right shoe and a left shoe from different pairs of shoes?)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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