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
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.