Question

Consider a football team with a 15-game schedule. Each game ends with a win (W), a loss (L), or a tie (T). Once the schedule is set, how many ways can the schedule end with 11 wins, 3 losses, and 1 ties?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the number of ways the schedule can end with 11 wins, 3 losses, and 1 tie, we can use the formula for combinations.

The total number of games played is 15, and we want to arrange 11 wins, 3 losses, and 1 tie within those 15 games.

The number of ways to choose the 11 games out of 15 for wins is given by the combination formula:
C(15, 11) = 15! / (11! * 4!) = 1365

Next, we need to choose the 3 games out of the 4 remaining games for losses:
C(4, 3) = 4

Finally, the outcome of the remaining 1 game is fixed because it must be a tie.

Therefore, the total number of ways the schedule can end with 11 wins, 3 losses, and 1 tie is:
1365 * 4 = 5460

So, there are 5460 ways the schedule can end with 11 wins, 3 losses, and 1 tie.