10 teams enter a soccer tournament. In the first round teams paired in 5 pairs to play with each other. How many different pairings are possible neither the order of the pairings nor the order of teams within each pairing matters?

There are 945 ways to make the pairings

Step-by-step explanation:

Lets pick a team. There are a total of 9 ways to select its pair. Now we have 8 teams remaining, note that the team we picked at the start doesnt matter because it will eventually be picked and the order doesnt matter. From the 8 teams remaining we select one of them and we pick a pair for it; we have 7 possibilities since we hace 7 teams remaining.

From the 6 teams remaining we take one of them and we select its partner, we now have 5 possibilities. From the 4 teams remaining we select one of them and pick 1 of the 3 teams remaining as its pair. Then, we pair the remaining teams.

This gives us a total of 9*7*5*3 = 945 ways to pair the teams.

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step-by-step explanation:

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