Question

There are 6 students in a classroom with 8 desks. How many possible seating arrangements are there? (The answer isn't 48 or 2, i tried that)

Answer 1

this is a problem in statistics that makes use of permutation. permutation is used since order or arrangement is significant in counting down the number of ways. this is different from combination which doesn't make use of order. In this case, the formula is 8P6 from nPr which is equal to 20160 ways, 

Answer 2

Answer: 20160

Step-by-step explanation:

Given : There are 6 students in a classroom with 8 desks.

Since here order matters , we use permutations.

The number of permutations of n objects taken r at a time is calculated by the following formula:

$^nP_r=\dfrac{n!}{(n-r)!}$

Then , the number of possible seating arrangements are :

$^8P_6=\dfrac{8!}{(8-6)!}=\dfrac{8!}{2!}=20160$

Therefore, the number of possible seating arrangements are 20160.