# How to combine possible permutations of two sets to find number of combined permutations

I hope the title accurately describes the question.

I have a question that asks:

There are 7 male swimmers and 5 female swimmers. If there is a gold, silver, and bronze medalist male swimmer, and a gold and silver medalist female swimmer, how many arrangements are possible?

Here's how I approached the problem:

I looked at the male swimmers first,

Gold medal = 7 possibilities Silver medal = 6 possibilities Bronze medal = 5 possibilities

7!/4! = 210 possible arrangements for the males

for females:

Gold medal = 5 possibilities Silver medal = 4 possibilities

5!/3! = 20

Now this is where I got kind of unsure about what to do....

I decided to think of the next step as two task,

task 1 = pick 3 boys, task 2 = pick 2 girls

task 1 = 210 options (number of permutations), task 2 = 20 options

so 210 x 20 = 4200......I think that number seems really high. Is there a proper method to use for this type of question? Or is it just kind of an combination of methods.

• You are correct to multiply them together. Like if you had 210 shirts and 20 pants and were looking for the number of outfits. For each of the 210 male arrangements, we have to pair it up with 20 female arrangements. – turkeyhundt Jan 27 '15 at 1:03
• You are correct. The male and female medal assignments are independent events (knowing one does not affect the other). This would not be the case, for instance, if there were one co-ed race which could be won by either a male or a female. In that case, knowing that a male had won changes the possibilities for women medals, and vice versa. – David G. Stork Jan 27 '15 at 1:10
• Thanks turkeyhundt and David, it's seems crazy how many permutations there can be of a rather small set! – Mike Jan 27 '15 at 1:16