# Easy Permutation-Combination Solved QuestionAptitude 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. Common Information Question: 4/4 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:

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

## (2) Comment(s)

Bet
()

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

Shireesh
()

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.