# There are 31 students in a class, number of girls is one more then number.........How many ways can such a team be made?

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There are 31 students in a class, number of girls is one more then number of guys.
We need to form a team of four students.
All four in the team cannot be from same gender and number of girls and guys in the team should not be equal.
How many ways can such a team be made?

posted Feb 21

15680 ways

Its obvious that number of girls= 16, boys= 15
Number 0, 2 and 4 in the teams excluded. So teams can be formed as 1 or 3 of the same gender:
1 boy + 3 girls -> Combination 1 of 15 x Combination 3 of 16 = 15 x 560 = 8400
3 boys + 1 girl -> Combination 3 of 15 x Combination 1 of 16 = 455 x 16 = 7280
total -> 8400+7280=15680

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