In how many ways can a group of 6 people be split into three teams of
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Updated on: 20 Jul 2021, 09:50
Total cases: 6!
Now we have to discard when in first place and in second place we have the same people exchanged.
For example: let's name people 1,2,3,4,5,6
one group combination could be:
12, 34, 56
another could be:
21, 34, 56
but this is the same case as the first one. The same occurs with the second and third group. This is why it must be divided by 2!*2!*2!.
Now we have to discard the order among groups.
For example in the 6! cases:
12, 34, 56
is different to
34, 12, 56
when it isn't in our question because the order among groups does not matter. So you have to divide by 3P3 which is the number of permutations of 3 groups grouped from 3 to 3.
Total: \(\frac{6!}{2!*2!*2!*3!} = 15\)