Asked by Keonn'a
From a group of 10 players a team 4 will be chosen for a dodgeball team. How many different teams are possible.
10 nCr 4 =210
but how can I work it out.
10 nCr 4 =210
but how can I work it out.
Answers
Answered by
Steve
There are 10 ways to choose the 1st member
9 ways for the next, etc.
So, there are 10*9*8*7 = 5040 ways
But, once they are chosen, the order does not matter, so divide that by 4! and you have 210.
That is, choosing people
1,2,3,4
1,2,4,3
1,3,2,4
1,3,4,2
...
There are 4! = 24 ways to choose them, but they are still the same team.
9 ways for the next, etc.
So, there are 10*9*8*7 = 5040 ways
But, once they are chosen, the order does not matter, so divide that by 4! and you have 210.
That is, choosing people
1,2,3,4
1,2,4,3
1,3,2,4
1,3,4,2
...
There are 4! = 24 ways to choose them, but they are still the same team.
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