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 all members of the same class? |

✖ A. |
20 |

✖ B. |
25 |

✖ C. |
30 |

✔ D. |
35 |

**Solution:**

Option(**D**) is correct

This part of the problem seems similar to the first three parts but it is very different.

Here we want 6 freshmen **or** 6 sophomores **or** 6 juniors.

The group cannot be all freshmen since there are only 5 freshmen.

Therefore, the group can be a group of 6 sophomores **or **6 juniors.

Number of groups of sophomores $= {^8C_6} = 28$

Number of groups of juniors$ = {^7C_6} = 7$

Since we want the number of groups of 6 sophomores **or **6 juniors, we want the sum of each of these possibilities:

$= 28 + 7 =35$

**Ram**

*()
*

the question said that the group should have all the members of the club. it never said the group should have members of "only" one club. In that case why cant we take $^5C_5*^{15}C_1$ along with $^8C_6$ and $^7C_6$.