If I have 7 button down shirts, 5 pairs of pants and 3 pairs of shoes that I can wear to work then how many different outfits can I wear on an individual day?

105 different outfits can wear on an individual day

Solution:

I have 7 button down shirts, 5 pairs of pants and 3 pairs of shoes that I can wear to work

To find: Number of different outfits can I wear on an individual day

First he has to decide on a pair of pants and he has 5 different choices

For each of those choices he has a choice of 7 different button down shirts, so that gives him 5 x 7 = 35 different pant/shirt combinations

For each of those 35 different pant/shirt combinations, he has 3 pairs of shoes he could select, so altogether he has 35 x 3 = 105 different outfits

In short we can say,

different outfits = 7 x 5 x 3 = 105

So there 105 different outfits can wear on an individual day