In a university, a committee is to be formed consisting of three biology instructors, two physics instructors, and four chemistry instructors. If the university has five biology instructors, six physics instructors, and seven chemistry instructors available, how many unique committees can be formed?

Answer Choices

Correct answer marked below

1210

6420

3600

3840

5250

Correct

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Official Explanation

Official

To determine the number of different committees that can be formed, we will break the process into stages. Stage 1: Choose 3 biology instructors from the 5 available. The number of ways to do this is given by the combination formula, which is 5C3. This equals 10 ways. Stage 2: Choose 2 physics instructors from the 6 available. The…

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Comments

SaiJul 2, 2024

thanks a lot

KHAug 21, 2024

thanks

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.