Five young women and three young men are friends. One night, each of the women calls one of the men, whom she chooses at random. Find the probability that exactly k men are called for k = 1,2, and 3.
I'm having trouble understanding why I got this answer, which apparently is correct.
This is what I did:
The number of ways to choose 1 man from 3 men is 3. Now, the number of ways for 5 women to choose the same man from
3^5). So then, choosing the same man is
So probability that exactly 1 man is called is
Now, if anyone could explain me how this answer is correct, that would be great. The largest part I am having trouble understanding is why do we use
3 choose 1 on top of
Also how would you do this for k=2 or 3? Thank you