There are 10 players in a chess group, and each player plays each of t

Question

There are 10 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?

A. 10
B. 30
C. 45
D. 60
E. 90

praveen192 · Accepted Answer

Total there are 10 players. 
Each player will play with another 9 players. But in this process, the play between 2 players will be counted twice and hence needs to be divided by 2.

So (10*9)/2=45. Option C.

Another way to look at it is to directly the number of ways of choosing 2 people from 10 as a game is played between 2 people. Hence 10C2 = 45.

Psiva00734 · Answer

10 players are there.
two players play one game with one another.

so 10C2=10*9/2
=45
SO OPTION C is correct

shasadou · Answer

this is how I approach this kind of problems as I struggle to apply combinatorics concept on that. I usually draw a table similar to the ones we used in our schoold tournaments. Please see the pic attached:

1. there are 10 players
2. each cross-section stands for the H2H game
3. grey depicts that we cannot play against ourselves (i.e. 1 vs. 1 and etc)
4. as long as we play only  once  the number of the below yellow squares is the total number of games. Otherwise if we were to play twice (home-away) the area on the other side of the grey row would also become yellow and thus the total number of games would 2x

5. mathematically this looks the following:

10*10  however since we do not play against each other this should be rather  10*9  = 90 games if we played twice.  90/2 = 45  - we face each other once.

ScottTargetTestPrep · Answer

The total number of games played is 10C2 = (10 x 9)/2! = 45.

Answer: C

bumpbot · Answer

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There are 10 players in a chess group, and each player plays each of t

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There are 10 players in a chess group, and each player plays each of t

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