bhumika.k.shah wrote:Twenty girls qualify for the girls' Baseball team. How many teams of 9 girls each
may be formed? For each team of 9 girls, in how many different ways can the 9
starting positions be assigned?
I seriously am blank as to how to start with the problem!
Let's look at this as 3 different questions:
1) how many different groups of 9 can be formed out of 20 people?
How to solve: use the combinations formula.
If you are choosing k items out of a group of n objects, there are n!/k!(n-k)! possible selections.
20C9 = 20!/9!11! (way too much math to appear on the actual GMAT other than in this form)
2) how many different ways can 9 people be arranged?
How to solve: use the simple permutations formula.
If you are arranging all the n members of a group, there are n! possible arrangements.
9! (too big a number to appear on the actual GMAT other than in this form)
3) how many different ways can we arrange 9 people out of a group of 20 people?
How to solve: use the permutations formula.
If you are arranging k members out of a group of n objects, there are n!/(n-k)! possible arrangements.
20P9 = 20!/(20-9)! = 20!/11! (way too much math to appear on the GMAT other than in this form)
* * *
For (3), we could also multiply the first two results:
20C9 * 9! = 20!/9!11! * 9! = 20!/11!
(since nPk = n!/(n-k)! and nCk = n!/k!(n-k)!, if we multiple nCk by k! we end up with the permutations formula).
