Question

There are 15 boys and 10 girls in your class. A four member committee is to be formed from the students
of your class. In how many ways this can be done if the committee consists at least three girls?

Answer 1

Answer on Question #57587 – Math – Combinatorics | Number Theory

Question

There are 15 boys and 10 girls in your class. A four member committee is to be formed from the students

of your class. In how many ways this can be done if the committee consists at least three girls?

Solution

$$C _ {1 5} ^ {1} \cdot C _ {1 0} ^ {3} + C _ {1 5} ^ {0} \cdot C _ {1 0} ^ {4} = \frac {1 5 !}{1 4 !} \cdot \frac {1 0 !}{3 ! 7 !} + \frac {1 5 !}{1 5 !} \cdot \frac {1 0 !}{4 ! 6 !} = 2 0 1 0.$$

Answer: 2010.

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