Combinatorics and Expected Value There are 15 candidates running for a given Senate seat, comprised of 10 men and 5 women. There are 32 polls, in which any of the candidates are equally likely to be ranked first, independently of the other polls (meaning the position of each candidate on any of the polls is purely random).
Find the expected value of the number of times that a woman will rank 1st in any of the polls.
I understand I need to find the probability of that any given woman will rank 1st in at least 1 of the polls, which I need direction on how exactly to approach. 

There is a $5/15 = 1/3$ chance that a woman is ranked first in a random poll because that's how many women there are and it's assumed be random who ranks first. Since all of the polls are random this means the expected number of women winning polls is $1/3 * 32 \approx 10.66$
