[SOLVED] Combination Problems (helpp)
I'm studying for a math test from this textbook and the bad thing about it is that there aren't any answers/explanations to learn/check from, so I was wondering if anyone can help me with the following problems...
1) The question basically asks how many ways can one form a committee of 3 out of 10 distinct people, if Elaine (one of the distinct 10 people) must be on the committee?
I was thinking that I should subtract all the committees that didn't have Elaine in them, from the total amount of committees that can be formed. So, is 10C3-9C3 correct?
2) Tell how many ways two of Beethoven's nine symphonies can be chosen for a concert program for each situation. (Order's not important)
a. The Ninth symphony can't be chosen.
So it would be 8C2?
b. The Second Symphony must be chosen.
Well, since it's a group of two, i decided to look at it in a logical way. If the Second Symphony is chosen, then there's only one more Symphony to pick to create the group of two. Therefore, the answer would be 8. However, I was wondering how I would do it if there was a larger group than 2 (a group which would be difficult to answer it logically).
c. The Ninth Symphony can't be paired with the third, sixth, or seventh.
First, I found the total # of the groups of two, and got 9C2. I'm not sure what to do next...
Thank you for your time! :D