What distribution has the random variable of this exercise? The exercise says: There are 35 women and 45 men in a school. From this population are selected first 10 students and after a second selection, a final group of 6 students is determined. What is the probability that in this last group there are at least 5 women?
At first I would say that it is hypergeometric, but it happens that it is like there is a sample of 6 within another sample of 10, and there I do not know what to do. Could you help me?
Thank you very much.
 A: How would selecting the first sample and then sampling from it change the probabilities from just taking a sample of six at the first draw? 
If you think there must be a difference, let's perform a little thought experiment; in fact let's conduct a series of related experiments. We have a deep bowl with 35 red and 45 green balls (otherwise identical) in it. Assume they're about the size of marbles (roughly a centimeter or so in diameter), so we can hold a dozen or more at one time.
Before each experiment, we mix the balls around thoroughly (after replacing any balls drawn on a previous experiment).
Experiment 1: We turn out the lights and draw out 10 balls and place them into a bag, from which we then draw six and (after turning on the lights again) look at them. (This is analogous to your original problem)
Experiment 2: We reach in and pull out 10 balls with one hand; without looking, we drop four of them back in, leaving six in hand.
Experiment 3: We reach in and grab 10 balls with one hand but leave our hand in the urn; we let four fall out and we take our hand out with the remaining six.
Experiment 4: We reach in to take some balls; our hand touches 10 of the balls, of which we take six.
Experiment 5: We reach in and stir the balls around a bit more -- we touch dozens of balls, we don't know how many, and pull out six.
Experiment 6: We reach in and draw out six balls.
Can you suggest which pair of consecutive experiments will have a different distribution for the six balls (assuming they're already well-mixed each time)? (And if so, why would the distributions of ball colors change there?)

If it's still not convincing that it makes no difference, consider a simpler case (one which is easy to enumerate all the possibilities for): 
(A) There are 2 red and 3 white balls. Draw 3. Then from that pool of 3 draw 2. What's the probability they're both red? 
... compare that with ... 
(B) There are 2 red and 3 white balls. Draw 2. What's the probability they're both red? 
Note that for (A) if you label the 5 balls A, B, C, D, E, the possible pools of 3 are (ignoring order):
ABC --> RRW
ABD --> RRW
ABE --> RRW
ACD --> RWW
ACE --> RWW
ADE --> RWW
BCD --> RWW
BCE --> RWW
BDE --> RWW
CDE --> WWW

of which the first three have two red. In those 3/10 cases, the chance of two reds in the second round is .... ?
