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Combination Confusion:

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Combination Confusion:

by chinspeaks » Thu Dec 15, 2016 7:40 am
Can someone please tell me why we go about answering these two questions differently? Any help would be appreciated!

1. From a total of 4 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

2. A small division of a company, with 25 employees, will choose a three person steering committee consisting of a facilitator, a union rep, and a secretary. How many different possible steering committees could be chosen?

I believe the first half of question 1 (either the girls or the boys probability) should be answered in the same fashion as question 2. But it's wrong. I'm just trying to figure out why.
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by [email protected] » Thu Dec 15, 2016 9:40 am
Hi chinspeaks,

In the future, you should make sure to post just one question per thread (so the discussion can stay focused on one prompt and we can avoid the confusion of criss-crossing discussions) and you should include the ENTIRE prompt (with the 5 answer choices).

That having been said, these two prompts are fairly standard combination/permutation questions (although the first one is a bit rarer of a prompt).

In the first prompt, we're creating committees without concern of who's chosen 'first', so the order of the 4 people doesn't matter - it's a group, so we should use the Combination Formula. Since we're choosing 2 boys from a group of 4 boys, there are 4C2 = 6 possible groups of 2 boys. The same goes for the number of girls... 4C2 = 6 possible groups of 2 girls. Each group of 2 boys could be paired with each group of 2 girls, so there are (6)(6) = 36 possible groups of 4 that can be created.

In the second prompt, the three 'positions' each carry a unique title (facilitator, rep and secretary), so we're dealing with a Permutation. Once one of the 25 people is placed in a position, there are fewer people available for the next position...

There are 25 people who could be facilitator. Once we place one....
There are 24 people who could be union rep. Once we place one...
There are 23 people who could be secretary.

Thus, there are (25)(24)(23) possible options.

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by Matt@VeritasPrep » Thu May 11, 2017 7:58 pm
The big distinction is whether order matters. You can think of a permutation as having TWO steps (choosing, then ordering) and a combination as having ONE (only choosing).

For instance, if I'm deciding to take three friends with me to a basketball game, and I have nine friends who want to go, that's a combination, because I'm only CHOOSING.

But if I'm taking three friends out of those nine, then deciding how the four of us are going to sit, that's a permutation: I'm CHOOSING, then ORDERING.
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