What is the probability that the photograph shows a woman in the middle flanked by two men, one on either side of her? From a set of three women and four men, three are chosen at random to stand in a row for a photograph. What is the probability that the photograph shows a woman in the middle flanked by two men, one on either side of her? my attempts:probability that the photograph shows a woman in the middle flanked by two men, one on either side of her $= \frac{2}{7}$. personally I don't know this from where I have to start. I'm completely struck. please help me.

Split it up into different problems. Firstly: exactly 2 men and exactly one woman must be chosen...so choosing 1 woman from a total of 3 is: $3 \choose{1}$ multiplied by choosing 2 men out of a total of 4: $4 \choose 2$.

Now the second part of the problem is this: after choosing the 3 people, how can they be arranged?: MWM, MMW, WMM, etc...since the one chosen woman MUST be in the middle, only the men on the sides can be arranged..so there are 2 possible "correct" arrangements, since it doesn't make a difference which of the two men is standing to her right.

So the total number of "correct" possibilities is: $${3\choose{1}}\cdot{4\choose{2}}\cdot2$$

All that is left is to divide that with the total number of possibilities to get the probability.