Permutation & Combination

[charlesdavid25]

In an IPL cricket competition, there are 9 teams. How many matches were held and in how many ways can each team play each other?

Please help.

[gmatpill]

You are trying to find the number of ways that each team can play with each other.

This is about combinations not permutations. Order does not matter.

So out of 9 teams, you want to pick 2, such that the order does not matter.
That's 9nCr2
That's 9! / (2! * (9-2)!)
= 9! / (2! *7!)
= 8*9 / 2
= 72/2= 36

[Chris Knight]

Quick way is (9 * 8)/2!Think how many teams can go in the 2 spots - 9 for the first, 8 for the second. Then divide by the number of spots factorial if it is a group. Leave it alone if it is a list.

[thepillow]

I agree with the answer, but I just wanted to offer another way to think about it:

To find the number of matches played if all teams play each other:

The 9 teams each played the 8 other teams = 9*8 =72

However, each time a match was played it counted for both teams that participated. So we've double counted. 72/2 = 36 total matches