SAT II math II C - help on this problem plz!

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Discus: SAT/ACT Tests and Test Preparation: May 2004 Archive: SAT II math II C - help on this problem plz!
 By Haruhara (Haruhara) on Monday, May 31, 2004 - 01:15 pm: Edit

there are 10 people. how many combinations are possible for one group of 7 people and one group of 3 people?

book says 120, but that seems to be the combo jobber of both nCr(10,7) and nCr(10,3)... so wouldn't you have to multiply 120 by 120 (they're both 120) to get total number of combos?

 By Qwert271 (Qwert271) on Monday, May 31, 2004 - 01:21 pm: Edit

When you pick the people for the 3 person group, that dictates which ones are in the 7 person group because they are the only ones left. You don't need to figure in the possibilities for the 7 person group.

If you think about it conceptually in terms of the 3 person group, you have 10*9*8 possibilities if the order matters. It doesn't, so you divide by 3*2*1.

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