Bunuel wrote:

Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256

B. 24

C. 15

D. 12

E. 4

The difficulty of combinatorial questions is usually in understanding how to do the calculation.

This requires an understanding of the underlying logic, e.g a Logical approach.

Cody has 4 items of clothing and he must choose at least 1 of them.

The simplest way to solve this question is to look at each item of clothing separately and ask 'Will Cody take it?'

That is - he can take or not take the sweatband - 2 options.

He can take or not take the socks - 2 options.

He can take or not take the jersey - 2 options and the same for the shorts - 2 options.

Each of these decisions is independent so multiplying all our options we hav 2*2*2*2 = 16 options.

Since Cody must take at least one item then the option where he takes nothing is impossible so there a total of 16 - 1 = 15 options.

(C) is our answer.

**A different solution would be to just brute force list all the options.

This works because there are only 4 items so there aren't too many different choices.

This approach is very good to avoid wasting time if you tend to get stuck on abstract questions.

_________________

David

Senior tutor at examPAL

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