Question

In a baseball tournament, teams get 5 points for a win, 3 points for a tie and 1 point for a loss Nathan’s team has 29 points how many different combinations of wins ties and losses can Nathan’s team have

Answer 1

Answer:

37 different combinations

Step-by-step explanation:

First of all, we will count the possible combinations that add up to 29.

-Losses only;

One possibility: 29 losses

-Ties & losses;

Nine possibilities: 1 tie and 26 losses; 2 ties and 23 losses; 3 ties and 20 losses;4 ties and 17 losses; 5 ties and 14 losses; 6 ties and 11 losses; 7 ties and 8 losses; 8 ties and 5 losses; 9 ties and 2 losses

-Wins & losses

Five possibilities: 1 win and 24 losses; 2 wins and 19 losses; 3 wins and 14 losses; 4 wins and 9 losses; 5 wins and 4 losses

Now, what we want to find from the question is number of possibilities for wins, ties, and losses all together. So, we will count up the ties and losses in the remainder for each case of a given number of wins.

Thus;

For 0 Wins: 0 ties and 29 losses; 1 tie and 26 losses; 2 ties and 23 losses; 3 ties and 20 losses;4 ties and 17 losses; 5 ties and 14 losses; 6 ties and 11 losses; 7 ties and 8 losses; 8 ties and 5 losses; 9 ties and 2 losses.

Which sums up to 10 possibilities

For 1 win; 0 ties and 24 losses; 1 tie and 21 losses........8 ties and 0 losses.

Which sums up to 9 possibilities

For 2 wins; 0 ties and 19 losses; 1 tie & 16 losses............ 6 ties and 1 loss.

Which sums up to 7 possibilities

For 3 wins; 0 ties and 14 losses; 1 tie and 11 losses ....... 4 ties and 2 losses.

Which sums up to 5 possibilities

For 4 wins; 0 ties & 9 losses; 1 tie and 6 losses....... 3 ties and 0 losses

Which sums up to 4 possibilities

For 5 wins; 0 ties and 4 losses; 1 tie and 1 loss

Which sums up to 2 possibilities

Thus;

Total number of possibilities of combinations of wins, ties and losses = 10 + 9 + 7 + 5 + 4 + 2 = 37