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
A PS Question on Permutations and Combinations
Subscribe / Share
Subscribe
B
ans) B
sol:
8c2 * 6c2 * 4c2 * 2c2
E
TAKE GMAT pl provide correct ans !
B is incorrect.
Hint:
The 4 teams, of 2 people each, are interchangeable.
E. take gmat team, please provide the answer
[8!/4!]/4*4=105
E
Few more attempts please!
B is indeed correct; the interchange funda here, is taken care of in the formula itself.
Alright friends, the answer and explanation here.
I am stating 3 approaches to solve the same problem. Pick whichever you like.
Approach 1:
1st team could be any 2 guys… there would be 4 teams (a team of A&B is same as a team of B&A)… possible ways 8C2 / 4.
2nd team could be any of remaining 6 guys. There would be 3 teams (a team of A&B is same as a team of B&A)… possible ways 6C2 / 3
3rd team could be any of remaining 2 guys… there would be 2 teams (a team of A&B is same as a team of B&A). Possible ways 4C2 / 2
4th team could be any of remaining 2 guys… there would be 1 such teams… possible ways 2C2 / 1
total number of ways…
8C2*6C2*4C2*2C2
———————
4 * 3 * 2 * 1
=
8*7*6*5*4*3*2*1
——————–
4*3*2*1*2*2*2*2
= 105 (ANSWER)…
Approach 2:
say you have 8 people ABCDEFGH
now u can pair A with 7 others in 7 ways.
Remaining now 6 players.
Pick one and u can pair him with the remaining 5 in 5 ways.
Now you have 4 players.
Pick one and u can pair him with the remaining in 3 ways.
Now you have 2 players left. You can pair them in 1 way
so total ways is 7*5*3*1 = 105 ways i.e. E
Approach 3:
Out of 8 people one team can be formed in 8c2 ways.
8c2*6c2*4c2*2c2= 2520.
Divide 2520 by 4! to remove the multiples ( for example: (A,B) is same as ( B,A) )
The answer is 105.
Possible ways in which a player can assciate with others-
12 13 14 15 16 17 18- 7 ways
23 24 25 26 27 28- 6 ways
similarly, possible ways to form team-
7*6*5*4*3*2*1= 5040
Now, we have to form 4 teams having 2 members each=
5040/(4*3*2*1*2)= 105
ans is E