Posted by Qi on Tuesday, August 20, 2013 at 6:57am.
They are 5 boys.If each boy plays a game of chess with each of the boys, how many games will there be?

Maths  Reiny, Tuesday, August 20, 2013 at 8:23am
Each of the five boys can play against each of the other 4. which would be 20 games,
BUT, that would include the pair of games of
boy1 vs boy2 and boy2 vs boy1, the same game.
So we have to divide by 2 to eliminate all those "doubles"
There will be 10 games
The number is actually low enough for you to list them
12
13
14
15
23
24
25
34
35
45 for a total of 10
This is a typical "combination" problem where you are choosing the number of cases of "5 choose 2" or
C(5,2) = 5!/(3!2!) = 10