From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?
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350 ways
- 420 ways
- 550 ways
- 720 ways
The correct answer is: A
Explanation
To form a committee of 2 girls and 3 boys from 5 girls and 7 boys:
Step 1: Combinations for Girls = \(^5C_2\) = \(\frac{5!}{(5-2)!2!}\) = 10
Step 2: Calculate the Combinations for Boys = \(^7C_3\) = \(\frac{7!}{(7-3)!3!}\) = 35
the total number of ways to form the committee, multiply the combinations of girls and boys: 10 x 35 = 350ways
The total number of ways to form the committee is: 350.
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