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by heshamelaziry » Mon Nov 16, 2009 4:21 pm
9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

OA 60
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by dmateer25 » Mon Nov 16, 2009 5:22 pm
The guards can be chosen in 6C3 ways.
The forwards can be chosen in 3C2 ways.

6C3 * 3C2

6C3 = 20
3C2 = 3

20 * 3 = 60
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by heshamelaziry » Mon Nov 16, 2009 7:11 pm
Is there a way to solve this by using total desired outcome / total outcomes ? or the same way this question is solved:


A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different.)

Whenever I see the word at least 1 I always go for the rule
Without restriction

Picking 3 from 10 ppl : 10c3 = 120 ---- MEANS 10i / 3i (10 – 3) i

Picking 3 without any Senior partner : 6c3 = 20-- MEANS 6i / 3i (6 – 3)i

No of ways with at least 1 SP = 120 - 20 = 100.
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