Combinatorics vs Permutations

[dinoush]

From the manhattan gmat practice exams:
9 Basketball players are trying out for a team, 5 are to be selected. If there are 6 guards and 3 forwards and only 3 guards and 2 forwards are to be chosen... How many different teams can be created?

Answer explains that 3 guards are to be selected from 6 multiplied by 2 forwards to be selected from 3. they solve it using combinatorics...



Why is that? Order does not matter in these cases does it? if you pick kid number 1 instead of kid number 2 with kid number 3... u still have 2 kids at the end of the count...

[ronaldramlan]

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[mschwrtz]

I have eliminated the example from GMAT Focus, the copyrighted property of GMAC. Please read and follow the guidelines. I have left our own example.

You're right, order doesn't matter. But this is not a 9 choose 5 question. You are actually making two sets of choices, one for the guards (6 choose 3) and one for the forwards (3 choose 2). No forward can be chosen for a guard spot, and no guard can be chosen for a forward spot.

Since any of the 20 groups of guards can form a team with any of the 3 groups of forwards, you have 20 times 3 possible teams.

For more, see page "Multiple Arrangements" on page 72 of your Manhattan GMAT Word Translations Strategy Guide.