How many different outfits can he select? (question)

Question

Hey, there. There's something that I don't understand about the answer to the following problem, which was posted on your site awhile ago: why don't we divide Selam's answer by 120 (1 x 2 x 3 x 4 x 5)? After all, this problem deals with combinations, not arrangements -- and there's no real difference between, say, red pants/yellow shirt/black jacket/white tie/shoes and yellow shirt/red pants/black jacket/white tie/shoes...

Shelby T.

asked • 09/10/15

How many different outfits can he select?

Tom has 4 pairs of pants, 5 different colored dress shirts, 4 sports jackets, 11 ties, and 1 pair of dress shoes in his closet. How many different outfits can he select?

Selam N.answered • 09/10/15

Mathematics Teacher

To begin solving, think of just the pants and the shirts;

each of the 4 pair of pants can be paired with one of the 5 shirts, giving you 4*5= 20 combinations.

 

Therefore, to apply this type of solution to all: 4 pair of pants, 5 dress shirts, the 4 sports jacket, 11 ties, and 1 pair of dress shoes,

(4)(5)(4)(11)(1)=880

there are 880 possible combinations.

Answer 1

Actually it is not a combination. It is a counting.

Have you ever made a counting tree?