GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
86 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 (3.8k points)  
retagged by | 86 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 (3.4k 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 (15.5k points)  


Top Users Sep 2017
  1. Habibkhan

    8312 Points

  2. Warrior

    2862 Points

  3. rishu_darkshadow

    2796 Points

  4. Arjun

    2766 Points

  5. A_i_$_h

    2526 Points

  6. manu00x

    2094 Points

  7. nikunj

    1980 Points

  8. Bikram

    1874 Points

  9. makhdoom ghaya

    1810 Points

  10. SiddharthMahapatra

    1718 Points


26,281 questions
33,842 answers
80,382 comments
31,192 users