Question

A tourist in Ireland wants to visit six different cities. How many different routes are possible?

Answer 1

Answer:

$6P6 = \frac{6!}{(6-6)!}=\frac{6!}{0!}= 6! =6*5*4*3*2*1=720$

D. 720

Step-by-step explanation:

For this case we have 6 different cities that needs to be ordered in different ways. And the best way to solve this problem is using permutations since we can't repeat the route.

We need to remember the concept of permutation.

A permutation, known as "arrangement number"  "is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself". Where S correspond to the sample space. And the formula is given by:

$nPX = \frac{n!}{(n-x)!}$

And for this case we have a total of 6 cities and we want to know how many routes with these 6 cities we can create, so then n=6 and k=6 and if we replace we got:

$6P6 = \frac{6!}{(6-6)!}=\frac{6!}{0!}= 6! =6*5*4*3*2*1=720$

And then we have 720 ways to visit six different cities. So the best option is:

D. 720