Question

A closet contains 5 shirts, 8 skirts, and 3 pairs of shoes. How many possible outfit combinations are there?

Answer 1

Presumably, an outfit consists of 1 shirt, 1 skirt, 1 pair of shoes, no more, no less, right?

Answer 2

So if we pick our favorite shirt, and our favorite skirt, and we have 3 different pairs of shoes, how many outfits can we make?

Answer 3

3

Answer 4

Right. Okay, if we stay with our favorite shirt, but we choose a different skirt, how many more outfits can we make?

Answer 5

3 more

Answer 6

Right again. For each combination of all but the last choice, we get as many outfits as there are options for the last choice. We have 3 pairs of shoes, so for each combination of skirt and shirt, we get 3 outfits.

What if we picked shoes and shirt first, how many outfits could we make for each combination of shoes and shirt?

Answer 7

15

Answer 8

uh, no. 1 pair of shoes, 1 shirt, and then we have 8 skirts to choose from. 1*1*8 = 8 different outfits, right?

Answer 9

For problems like these, where each thing is chosen independently of the others, the total number of different combinations is simply the number of choices for each thing multiplied together. So if we have 2 shirts, 3 skirts, and 4 pairs of shoes, we have
\[2*3*4 = 24\]different combinations we can put together.

Given that information, how many outfits can you put together from the 5 shirts, 8 skirts, and 3 pairs of shoes mentioned in your problem?

Answer 10

oh so you miltiply all options together so the answer to the question would be 1020

Answer 11

120

Answer 12

Yes, that is correct.

Answer 13

thank you

Answer 14

You could also systematically make a list of all of the combinations, and count them. If you think about it, this is really like putting together numbers from digits.

You have 10 digits, 0,1,2,3,4,5,6,7,8,9

If you have a 1 digit number, you can have 10 different numbers
If you have a 2 digit number, you can have 10 1 digit numbers each followed by 10 different 1 digit numbers, or 10*10 = 100 numbers.

If you wanted to know how many numbers you could make that start with 1 or 3 and have 2 digits, you would say "the first digit has 2 choices, 1 or 3, and the second digit has 10 choices, 0-9, so I can make 2*10 = 20 numbers that start with 1 or 3"