# 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: 1/4 How many combinations of students are possible if the group is to consist of exactly 3 freshmen?
 ✖ A. 5000 ✔ B. 4550 ✖ C. 4000 ✖ D. 3550

Solution:
Option(B) is correct

Here we need the number of possible combinations of 3 out of 5 freshmen,${^ 5C_3}$, and the number of possible combinations of 3 out of the 15 sophomores and juniors, ${^{15}C_3}$.

Note that we want 3 freshmen and 3 students from the other classes.

Therefore, we multiply the number of possible groups of 3 of the 5 freshmen times the number of possible groups of 3 of the 15 students from the other classes.

${^ 5C_3} × {^{15}C_3} = 4,550$

## (4) Comment(s)

David
()

Good question!! Keep it up..:)

Asmita
()

easy to understand!!!

!vry helpful 4 me.....

without any teachereasy to understand!!!!

Ur Mum
()

Good one.

Samar
()

suggest alternative to the solution..it's still not clear to me..