Question

Bob, Sue, Larry, Sally and Fred are waiting in lime to buy concert tickets.
(1) In how many different ways can they stand in line?

(2) How many ways can they line up if Larry insists on being in the middle?

Answer 1

Answer:

1) 120

2) 24

Step-by-step explanation:

This is a problem involving permutations: the number of different ways you can arrange stuff

If there are n items, n! represents the permutation of n and is given by the formula : 1 x 2 x 3 x........x (n-1) x n also sometimes written in the form
n x (n-1) x (n-2) x........x 3 x 2 x 1

In this case there are 5 people. So the number of different ways they can stand in line is 5! = 5 x 4 x 3 x 2 x 1 = 120 ways  Answer to (1)

Answer to (2)
If Larry insists on being in the middle the other 4 have to arrange themselves around Larry in 4! ways = 4 x 3 x 2 x 1 = 24 ways