Aptitude 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. |
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 |

**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.

${^5C_2} × {^8C_2} × {^7C_2}= 5,880$

**Anusha**

*()
*

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.

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