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 M1, M2, W1 and W2 are selected players for the mixed double tennis game.

If  M1 chooses W1, then M2 has W2 as the partner or if  M1 chooses W2, then M2 has W1 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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 1. In double tennis game 4 players can play.

 1st case :  6C0(4C4)4!=24

 2nd case:  6C1(4C3).4!=576

3rd case:    6C2(4C2).4!=2160

4th case:    6C3(4C1).4!=1920

5th case:    6C4(4C0).4!=360

so required no=24+576+2160+1920+360=5040

2. If one team played match with every other team than no. of teams = 153C2=11628

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