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I'm having a hard time understanding a small part of the following problem

Problem: We are choosing 4 people from 7 women and 4 men. How many ways are there to form the committee if at least two are women?

So if my thinking is correct here, we don't differentiate between the 7 women and the order at which we pick these people don't matter, am I correct in assuming this?

So for example, in the case where my 4 chosen people consists of 4 women, would I differentiate between [W1, W2, W3, W4] and [W1, W3, W5, W7] and would I be differentiating between [W1, W2, W3, W4] and [W4, W3, W2, W1].

in the first example, both consist of 4 women but different women and in the second example, they both consist of the same people but in different order.

I asked my T.A about this but he just told me that we care about how many different ways there are to have at least two women which didn't really help me understand the question any better.

Edit: So my thought was that since I am given the number of women and men there are, I would care about the uniqueness of the women and men but not the order at which they are chosen, There would be no reason to tell me the number of men and women if it didn't matter because the answer would then just be [W,W,M,M], [W,W,W,M] and [W,W,W,W] but given the number of women there are I would have to consider the fact that the group made of 4 women could be made from any number of women. Correct me if I'm thinking wrong here.

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    $\begingroup$ $p=\binom 7 2 \binom 4 2 +\binom 7 3 \binom 4 1 +\binom 7 4$ $\endgroup$ – Isham Jan 11 '18 at 14:54
  • $\begingroup$ So then the order doesn't matter but the uniqueness of the individuals does matter correct? @ Isham $\endgroup$ – AFC Jan 11 '18 at 14:55
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    $\begingroup$ What makes you think the order matters? As phrased, I agree that it doesn't sound like order matters, but maybe you have left something out. $\endgroup$ – lulu Jan 11 '18 at 14:55
  • $\begingroup$ For instance, if the positions had titles (e.g. "President", "Treasurer", etc.) then order would matter. $\endgroup$ – lulu Jan 11 '18 at 14:56
  • $\begingroup$ @user2142581 as Lulu clearly eplained it dosent matter $\endgroup$ – Isham Jan 11 '18 at 14:57
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Edit: Isham is correct.

Break the problem down into scenarios in which 2, 3, and 4 women are included in the committee. The number of configurations of women multiplied by the configurations of men results in the number of unique committees.

For instance, a committee comprised of two women and two men has:

(7 choose 2)*(4 choose 2) configurations. The order of the women and men don't matter, but these do represent unique combinations.

(7 choose 2)(4 choose 2) + (7 choose 3)(4 choose 1) + (7 choose 4)*(7 choose 0) = 301.

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I think you're correct that different women are considered distinguishable, but the order does not matter.

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