GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
50 views

According to my understanding, there should be men and women both in the team. So we can do:
3M and 1W or
2M and 2W or
1M and 3W.

So it will be: C(5,3)*C(5,1)+C(5,2)*C(5,2)+C(5,1)*C(5,3).

But the answer given is 600. How is it possible?

asked in Probability by Loyal (3.4k points)   | 50 views

2 Answers

+1 vote
Best answer
A mixed pair in a tennis match consists of 1 man and 1 woman. To form the team you have to select 4 pairs of 1 man and 1 woman.So there'll always be 4 men and 4 women in team. Hence your approach is incorrect.

So suppose you have 5 men: M1, M2, M3, M4, M5 and 5 women: W1, W2, W3, W4, W5

Now, for first pair if you select a man, you have 5 options for women to form a team.

For second pair, if you select a man, you have 4 options for women (one women already formed the team, so she can't be included in any other team)

Similarly, for 3rd pair, you have 3 options and 4th pair you have 2 options.

Now from 5 men, you have to select 4 [e.g.you can select M1, M2, M3, M4 or M2, M3, M4, M5 or ... ] i.e., $5 \choose 4$

So total possible number of selections:  $5 \choose 4$ * 5 * 4 * 3 * 2 = 5 * 120 = 600
answered by Loyal (3.1k points)  
selected by
+1 vote

Here, they are asking In how many ways the pairing can be done?

First, select 4 men and 4 women. Thaat can be done $\binom{5}{4}$ * $\binom{5}{4}$

Now, once selected, they can be arranged in 4! ways (i.e. onto functions from 4 men to 4 women)

So, asnwer = $\binom{5}{4}$ * $\binom{5}{4}$ * 4! ways

                 = 600 ways

answered by Veteran (11.6k points)  
Top Users Jan 2017
  1. Debashish Deka

    9872 Points

  2. sudsho

    5596 Points

  3. Habibkhan

    5498 Points

  4. Bikram

    5350 Points

  5. Vijay Thakur

    4508 Points

  6. Arjun

    4458 Points

  7. Sushant Gokhale

    4410 Points

  8. saurabh rai

    4236 Points

  9. santhoshdevulapally

    3906 Points

  10. Kapil

    3892 Points

Monthly Topper: Rs. 500 gift card

19,480 questions
24,260 answers
54,207 comments
20,405 users