Aptitude Discussion

**Common Information**

There are $5$ freshmen, $8$ sophomores, and $7$ juniors in a chess club. Find the number of orders in which the $6$ students from this club can win the first six prizes:

Q. |
If all students attend the competition and the winners are all members of the same class. |

✖ A. |
21,200 |

✖ B. |
23,200 |

✔ C. |
25,200 |

✖ D. |
27,200 |

**Solution:**

Option(**C**) is correct

In this case the 6 students are all from the same class and we can use permutations directly.

Number of orders of freshmen $= 0$

Number of orders of sophomores $= {^8P_6} = 20,160$

Number of orders of juniors $= {^7P_6} = 5,040$

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

$0 + 20,160 + 5,040 = 25,200$

**Bet**

*()
*

Hey Bet,

Without even looking at the other problems you may decide whether this is a problem on permutation or combination.

To do this you need to know the FUNDAMENTAL PRINCIPLE OF COUNTING.

You may read moore about it here: www.lofoya.com/Aptitude-Questions-and-Answers/Permutation-and-Combination/intro

how did this problem became permutation when the latter problems pertaining to winning are combination?