Mario goes shopping

Probability Level 2

Mario needs a new suit, consisting of pants and a jacket. The first store he visits sells 4 4 pants and 3 3 jackets. The second store he visits sells 7 7 pants and 9 9 jackets. The third store he visits sells 6 6 pants and 12 12 jackets. If Mario is willing to get his pants and jacket at different stores or at the same store, how many different pant/jacket combinations can he buy?


The answer is 408.

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Arron Kau by Arron Kau

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3 solutions

Alvin Willio
Aug 19, 2013

First, we know that the total of pants are

4 + 7 + 6 = 17 4 + 7 + 6 = 17 pants

and the total of jackets are

3 + 9 + 12 = 24 3 + 9 + 12 = 24 jackets

so we know how many different pant/jacket combination by multiplying the total of pants and jackets. so we get

17 ∗ 24 = 408 17 * 24 = 408 combinations

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Simple, and precise. I didn't really need to write a solution, now did I.

Great Job

David Kroell - 7 years, 9 months ago
Mariel Perez
Aug 18, 2013

To get the number of different combinations Mario can choose from, multiply total number of pants from all the stores by the total number of jackets from all stores.

(4+7+6) * (3+9+12)

= 17 * 24

= 408 combinations

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Kishlaya Jaiswal
Aug 19, 2013

He can choose only 1 jacket out of 24 and only 1 pants out of 17. So total combinations of pants and jacket that can made = ( 17 1 ) . ( 24 1 ) = ( 17 ! 16 ! ) . ( 24 ! 23 ! ) = 17.24 = 408 {17 \choose 1}.{24 \choose 1} = (\frac{17!}{16!}).(\frac{24!}{23!}) = 17.24 = 408 ways

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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