A Person Has 9 Friends, 4 of Whom are Male. In How Many Ways Can He GMAT Problem Solving

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?

  1. 32
  2. 96
  3. 286
  4. 120
  5. 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:

  1.  There can be 2, 3, or 4 males within the given constraints.
  1.  There can be 3, 2, 1, or 0 females within the given constraints.
  1.  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.)
  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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