Permutation-Combination
Aptitude

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Common Information

There are $5$ freshmen, $8$ sophomores, and $7$ juniors in a chess club. A group of $6$ students will be chosen to compete in a competition.

Q.

Common Information Question: 2/4

How many combinations of students are possible if the group is to consist of exactly 3 freshmen and 3 sophomores?

 A.

360

 B.

460

 C.

560

 D.

660

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Solution:
Option(C) is correct

This second part of the problem is similar to the first except that the choice of the second group of 3 comes only from the sophomores.

Again we want 3 freshmen and 3 sophomores so we multiply the number of groups of freshmen times the number of groups of sophomores.

${^5C_3} × {^8C_3} = 560 $


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