Question: A person has 9 friends, 4 of whom are male. In how many ways can he plan a trip so that there are at least 2 other male friends, but not more than 3 females?
- 32
- 96
- 286
- 120
- 250
Correct Answer: C
Solution and Explanation
Approach Solution 1:
There is only one way to solve this problem.
Given:
- The person has 9 friends
- 4 of them are male
Conditions:
- A trip needs to be planned with
- Atleast 2 other male friends
- Not more than 3 female friends
Find out:
- In how many ways the trip can be planned
Let us consider the above conditions and try to make the group:
- There can be 2, 3, or 4 males within the given constraints.
- There can be 3, 2, 1, or 0 females within the given constraints.
- Now, if wr run the combinations for males and females independently:
We get:
4C2, 4C3, 4C4 and 5C3, 5C2, 5C1, 5C0. (C - Combinations)
The results are = 6, 4, 1, 10, 10, 5, and 1, respectively. (We have to remember that 0! = 1.)
- Now, we multiply each "male" count with each "female" count and add:
First combination: 6∗10+6∗10+6∗5+6∗1=156
Second combination: 4∗10+4∗10+4∗5+4∗1=104
Third combination: 1∗10+1∗10+1∗5+1∗1=26
Total combinations: 156+104+26=286
The trip can be made in a probable 286 combinations
Hence, C is the correct answer.
“A person has 9 friends, 4 of whom are male. In how many ways can he”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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