6 In a particular softball league each team consists of 5
women and 5 men. In determining a batting order for 10
players, a woman must bat first, and successive batters
must be of opposite sex. How many different batting orders
are possible for a team
Answers
Given : In a particular softball league each team consists of 5 women and 5 men. In determining a batting order for 10 players, a woman must bat first, and successive batters must be of opposite sex.
To Find : How many different batting orders are possible for a team
Solution:
a woman must bat first, and successive batters must be of opposite sex.
Hence WMWMWMWMWM this would the order
5 W can be arranged in 5! = 120 ways
5 M can be arranged in 5! = 120 Ways
Total Ways = 120 * 120 = 14400 ways
14400 different batting orders are possible for a team
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