In order to participate in a quiz competition, seven students are to be selected randomly from a class of 12 girls and 10 boys. If there should be at least five girls in the team, then in how many ways the team can be selected?
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Given : seven students are to be selected randomly from 12 gi rls and 10 boys
at least five gi rls in the team
To Find : Number of ways
Solution:
gi rls = 12
Bo ys = 10
Team = 7
Atlea st gi rls = 5
5 gi rls + 6 gi rls + 7 gi rls
5 gi rls and 2 Bo ys = ¹²C₅*¹⁰C₂ = 792 * 45
6 gi rls and 1 Bo y = ¹²C₆*¹⁰C₁ = 924 * 10
7 gi rls and 0 Bo ys = ¹²C₇*¹⁰C₀ = 792 * 1
Total ways = 792 * 45 + 924 * 10 + 729 * 1
= 42,774 ways
Te am can be selected in 42,774 ways
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