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
