Question

One afternoon, they get together to play singles matches (one-on-one competitions).Every member of the club plays one match with another member of the club, so twentymatches are held. In how many ways can this be arranged?

Answer 1

Answer:

${40\choose 2}*{38\choose 2}*...*{2\choose 2}$

Step-by-step explanation:

20 matches, so there is 40 players in the club.

First number too chole 2 first players for match you can do it in ${40\choose 2}$.

Now you have 38 players, becaus you chose 2. Now frim 38 player you can choose new 2 in ${38\choose 2}$ ways. So and on... you will have ways to choose 20 matches in:

${40\choose 2}*{38\choose 2}*...*{2\choose 2}$.