# QA – Placement Quizzes | Permutation and Combination | Question 5

In how many ways can an interview panel of 3 members be formed from 3 engineers, 2 psychologists and 3 managers if at least 1 engineer must be included?

**(A)** 30

**(B)** 15

**(C)** 46

**(D)** 45

**Answer:** **(C)** **Explanation:** The interview panel of 3 members can be formed in 3 ways by selecting 1 engineer and 2 other professionals, 2 engineers and 1 other professionals and all 3 engineers.

- 1 engineer out of 3 engineers and 2 other professionals out of 5 professionals can be selected as

=^{3}C_{1}*^{5}C_{2}= 3 * 10 = 30 ways. - 2 engineers out of 3 engineers and 1 other professional out of 5 professionals can be selected as

=^{3}C_{2}*^{5}C_{1}= 3 * 5 = 15 ways. - 3 engineers out of 3 engineers and 0 other professional out of 5 professionals can be selected as

=^{3}C_{3}*^{5}C_{0}= 1 way.

Hence, total number of ways = 30 + 15 + 1 = 46 ways.

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