A group of 8 friends wants to play double tennis. How many

Question

A group of 8 friends wants to play double tennis. How many different ways can the group be divided into 4 teams of 2 people?

a) 420
b) 2520
c) 168
d) 90
e) 105

walker · Answer

N=\frac{C^8_2*C^6_2*C^4_2*C^2_2}{P^4_4}=\frac{4*7*3*5*2*3*1}{4*3*2*1}=105

mandy12 · Answer

Hi Walker,

What is the logic behind 4P4 ?

walker · Answer

When we choose four groups, it is necessary to exclude order among groups, for example:

12,34,56,78 and 34,12,56,78 is the same option. (1,2,3,4,5,6,7,8 - people)

ritula · Answer

Can u explain the logic behind this formula?

walker · Answer

C^8_2  - choose first team

C^6_2  - choose second team

C^4_2  - choose third team

C^2_2  - choose fourth team

P^4_4  - exclude order among four teams.

vd · Answer

Pretty good explanation Walker

FN · Answer

for some reason i get 115..

i did as follows..  /4!

i use 4! because suppose each player is a nd B..then we have counted that pair twice i.e ab, ba etc for each of the 4 slots..

barfer · Answer

maybe I'm not so skilled in combinative formulas but for me this is the way: for even N the quantity of pairs = (N-1)*(N-3)*...*(N-n), where n = N-1. So that for 8 players it's 7*5*3*1=105. For N=10 it's 9*7*5*3*1 = 945 P.S. I should explain how I reached that. I draw a picture with 4 lines then investigated those combinations, it was 3. Why 3, cause if we chosen 1 pair only 1 pair left. How many first pairs I could chose - 3 (N-1). OK, how about 6? I chosen 1 pair and what I saw, right, 4 lines. I had already seen them and knew that they consisted 3 possible pairs. How many first pairs I might chose, correct, 5 (N-1). So that we had (N-5)*(N-3)*(N-1). I kept reasoning and found the regularity and wrote it in the opposite way - see above

. All this reasoning took around 1 minute...

A group of 8 friends wants to play double tennis. How many

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards