Question

A company has 12 salespeople. A board member at the company asks for a list of the top 4 salespeople, ranked in order of effectiveness. How many lists are possible? Assume that the order of the salespeople on the list is relevant.

Answer 1

Since we have to take into consideration the order of the salespeople, we will the concept of permutation i.e., we will find the no. of ways of getting an ORDERED subset of r elements from a set of n elements.

The formula for this is given as

nPr= n!/ (n-r)!

Now, in this problem we have to select 4 salespeople out to 12 salespeople. Thus, here, we have n=12 and r= 4.

Hence nPr= 12p4= 12!/ (12-4)!

= 12!/ 8!

= 12*11*10*9

= 11880.

Hence, 11880 lists are possible.