A coed soccer team has W women and M men on the team. If 4 women and

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
The two posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.

Let's choose values for W and M and then answer the question.
Let W = 1 and let M = 1
So, to start, the team consists of 1 woman and 1 man.

4 women and 2 men are added to the team roster...
Now the number of women on the team = 1 + 4 = 5
And the number of men on the team = 1 + 2 = 3
So, there are 8 people on the team

...if one person on the team is selected at random to serve as team captain, then the probability that the team captain will be a woman can be represented as
There are now 8 people on the team and 5 are women.
So, P(a woman is selected) = 5/8

So, when we INPUT W = 1 and M = 1, the answer to our question (i.e., the OUTPUT) is 5/8

Now, we'll check each answer choice, and see which one yields an OUTPUT of 5/8 when we replace W with 1 and M with 1

A. (1 + 4)/(1 + 1 + 6) = 5/8 - PERFECT - KEEP A
B. (1 + 4)/(1 + 1 + 2) = 5/4 - No good. ELIMINATE B
C. (1 + 4)/(1 + 2) = 5/3 - No good. ELIMINATE C
D. (1 + 4)/(1 + 1) = 5/2 - No good. ELIMINATE D
E. 1/1 = 1 - No good. ELIMINATE E

Answer: A

Cheers,
Brent