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 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 $