1.Find the number of ways in which a mixed double tennis game can be arranged between 10 players consisting of 6 men and 4 women

2. In a hockey tournament , a total of 153 matches were played. If each team played one match with every other team, find the total number of teams that participated in the tournament

1.

Number of ways to select two men out of six men

Number of ways to select two women out of four women

Number of ways of selecting the players for the mixed double

Let M_{1}, M_{2}, W_{1} and W_{2} are selected players for the mixed double tennis game.

If M_{1 }chooses W_{1}, then M_{2} has W_{2 }as the partner or if M_{1 }chooses W_{2}, then M_{2} has W_{1 }as the partner.

∴ There are two choices for the teams.

Thus, Number of ways in which mixed double tennis game be arranged = 90 × 2 = 180

2.

Let the number of teams participating in the tournament be *n*.

Number of matches played between the teams

Thus, the number of teams participating in the tournament is 18.

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