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| Math Central | Quandaries & Queries |
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Question from Payal: A soccer team plays six games in one month. Each game results in a win, loss, or tie. For this soccer team, how many different sets of results are possible for the six games? |
Hi,
After the first game the team the team's record was win (W), loss (L) or tie(T). Three possibilities. Regardless of their record so far there are three possibilities for the second game. Hence after the second game there are $3 \times 3 = 9$ possible records. they are
WW
WL
WT
LW
LL
LT
TW
TL
TT
Again, regardless of the record so far there are 3 possibilities for the third game and hence after the third game there are $3 \times 3 \times 3$ possible records.
Can you complete the solution?
Penny
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