Question: If 4 women and 6 men work in the accounting department, in how many ways can a committee of 3 be formed if it has to include at least one woman?

1. 36
2. 60
3. 72
4. 80
5. 100

“If 4 women and 6 men work in the accounting department, in how many ways can a committee of 3 be formed if it has to include at least one woman?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.
To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach Solution 1
There is only one approach solution to this problem

Let’s say we have three spaces to fill:

\(\underline{A}\underline{B}\underline{C}\)

Case 1: Two men “AND” one woman. Whenever we have “AND”, we multiply.

So, \(^6C_2*4=60\)

Case 2: One man and two women

So, \(^4C_2*6=36\)

Case 3: All 3 women.

So, \(^4C_3=4\)

Now, we can have either of these choices. MMF “OR” MFF “OR” FFF. We add them in case of “OR”.

That gives us:
60 + 36 + 4 = 100

Correct option: E

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