If 4 Women and 6 Men Work in the Accounting Department GMAT Problem Solving

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

Suggested GMAT Problem Solving Questions

• Find the value of a. Given a=\(\sqrt{3\sqrt{3\sqrt{3\sqrt{3}}}}....\) GMAT Problem Solving
• Frances Can Complete a Job in 12 hours, and Joan Can Complete the Same Job in 8 Hours GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines can Produce a Total of 270 Bottles Per Minute. GMAT Problem Solving
• How Many Litres of a 90% Solution of Concentrated Acid Needs to be Mixed with a 75% Solution GMAT Problem Solving GMAT Problem Solving
• After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving
• If n = \(3^8\)– \(2^8\), Which of the Following is Not a Factor of n? GMAT Problem Solving
• What is the Remainder When \(3^{35}\) is Divided by 5? GMAT Problem Solving
• \(\frac{15^{11}-15^{10}}{14}=?\) GMAT Problem Solving
• What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Problem Solving
• If abc ≠ 0 is (a/b)/c = a/(b/c) GMAT Problem Solving
• If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving
• The Interior Angles of a Polygon are in Arithmetic Progression GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
• If 69% of k is 23, approximately how much is 23% of k? GMAT Problem Solving
• If \(2^{98}=256L+N\) , Where L and N are Integers and \(0 \leq N \leq 4\) , What is the Value of N? GMAT Problem Solving
• What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6? GMAT Problem Solving
• For How Many Values of k is 12^12 the Least Common Multiple GMAT Problem Solving
• Is Square Root = Always Positive? GMAT Problem Solving