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16 teams are taking part in a sports tournament and a draw is about to take place. For simplicity lets say that the teams in each pot are from the same part of the country eg East1, East2, East3, East4 meaning the pots pre draw look like this

[N1, N2, N3, N4] [E1, E2, E3, E4] [S1, S2, S3, S4] [W1, W2, W3, W4]

In the draw a team from each pot will be drawn and placed in a group, so that at the end there will be 4 groups each with 4 teams from different parts of the country

My question is how many different combinations of the entire draw are possible?

Montgomery Brewster
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2 Answers2

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You have four choices for the North. For each of those, you have four choices for the East. And so on. Therefore there are $4^4=256$ possible configurations.

Edit: I misread the question, the above gives the number of different groups that can be formed. I agree with @stretch's answer.

Bobson Dugnutt
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For the first group there are 4 choices from each of 4 parts of the country, or 256 choices. The second group has 3 choices from each part. 3^4 or 81 choices. Third group has 2^4 or 16 choices. Fourth group has what's left: 1 choice. 256+81+16+1 or 354 choices overall.

stretch
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