# Easy Permutation-Combination Solved QuestionAptitude Discussion

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

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.

${^5C_3} × {^8C_3} = 560$