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: 3/4

How many combinations of students are possible if the group is to consist of an equal number of freshmen, sophomores, and juniors?

 A.

5880

 B.

6880

 C.

7880

 D.

8880

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Solution:
Option(A) is correct

An equal number of students from each of the three classes mean 2 students from each class, that is, 2 freshmen and 2 sophomores and 2 juniors.

${^5C_2} × {^8C_2} × {^7C_2}= 5,880$


(2) Comment(s)


Anusha
 ()

Why should we consider only two students. Can't we consider 3 or 4 or 5.


Aarti
 ()

Because a group of 6 students is to be formed and the group has to consist of an equal number of freshmen, sophomores, and juniors. Only way possible is picking 2 students from each of freshmen, sophomores, and juniors.

If we consider 3 or 4 or 5 as you suggested then it will not be possible to form a group of six students keeping the requirements satisfied.