Team selection

[StoneBlack]

A group of 8 friends want to play doubles 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

[rijul007]

A group of 8 friends want to play doubles 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

no of ways of selecting 2 people from 8 = 8C2 = 28
no of ways of selecting 2 from remaining 6 = 6C2 = 15
no of waays of selecting 2 from 4 = 4C2 = 6
the remaining 2 will form a team

total no of selections = 28*15*6 = 28 * 90 = 2520

Option B

[shankar.ashwin]

The order in which the 4 teams are selected doesnt matter here..

So, its (8C2*6C2*4C2*2C2)/4! = 2520/24 = 105 E

[LalaB]

@rijul007 u should divide it by 4!


my approach 7*5*3*1=105

or use the formula (mn)!/(n!)^m*m!=(4/2)!/(2^4)*4!=7*5*3=105

[StoneBlack]

Thanks guys for replying.
The answer indeed is 105.

I cannot understand the logic applied to divide by 4!.Could you elaborate more on this?
Thanks.

[shankar.ashwin]

Hope this post clarifies
https://www.beatthegmat.com/doubles-t8119.html

Thanks guys for replying.
The answer indeed is 105.

I cannot understand the logic applied to divide by 4!.Could you elaborate more on this?
Thanks.

[LalaB]

Thanks guys for replying.
The answer indeed is 105.

I cannot understand the logic applied to divide by 4!.Could you elaborate more on this?
Thanks.

hm, will try to explain

for example , u have A B C D E F G H . grouping them in this way AB CD EF GH is the same as EF CD AB GH

[GMATGuruNY]

Check my posts below:

https://www.beatthegmat.com/combination-t92104.html

https://www.beatthegmat.com/a-group-of-8 ... tml#359208

https://www.beatthegmat.com/forming-teams-t73034.html