1. [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...

2. Originally Posted by ixcrazy
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?
If you have to pick this person then 9 people remain. And you need to choose 2 more. Thus, 9C2.

3. Originally Posted by ixcrazy
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)
c. The Ninth Symphony can't be paired with the third, sixth, or seventh.
Consider two cases.
First: how many cases are there the in which the ninth is included?
Second; how many cases are there the in which the ninth is not be included?
Then add those to get the number of favorable cases.