I'm having a hard time trying to determine when to use combination and when to use permutation with a problem. Can someone offer a clear and concise explanation or general rules to follow so I don't get tripped up on similar problems?
For example: How many ways are there to select five players from a 10-member tennis team.
My approach would be that there are 10 ways to choose the first spot, 9 for the second, 8 for the third… so the total is 10!/5!; but apparently this is a combination problem.
I'm just having a hard time telling the difference between the two. Are there any questions I can ask myself before I begin to really solidify what the problem is asking for?
Thank you!
EDIT:
Here's another problem I'm confused with:
Suppose that there are 9 faculty members in the mathematics department and 11 in the computer science department. How many ways are there to select a committee to develop a discrete mathematics course at a school if the committee is to consist of three faculty members from the mathematics department and four from the computer science department?
Why is the answer 9!/(3!6!) * 11!/(4!7!) rather than 9!/(3!6!) + 11!/(4!7!)?
Best Answer
Regular rule, Permutation is when order matters. You can memorize it with P ermutation-P osition. Combination on the other hand doesn't care in which order the elements are chosen.
As in your first example, you want to choose $5$ players, but no other information is given so you assume order isn't important.
Note that I the problem stated $5$ player to form a hockey team, then order could have mattered, for say center, Left and right wing, and left and right D player.
For your second example, note that for each subcomitee of $3$ members of math, there are $11!/(4!7!)$ subcomitee of members of CS so you have to multiply them