The Downtown Theater has 1 ticket window. In how many ways can 4 people
line up to buy tickets?
There are 4 people who can line up at the first position, but then only 3 people left to line up at the second position, only 2 people left to line up at the third position, and finally only 1 person left for the last position. Therefore, the total number of ways for 4 people to line up in a queue is:
4 x 3 x 2 x 1 = 24 ways.
In order to find out how many ways 4 people can line up to buy tickets at the Downtown Theater, we can use the concept of permutations.
Since there is 1 ticket window, the order in which the 4 people line up matters.
Therefore, we can calculate the total number of ways using the formula for permutations: P(n, r) = n! / (n - r)!
Here, n is the total number of people (4) and r is the number of people lining up (4).
Using this formula, we can calculate the number of ways as follows:
P(4, 4) = 4! / (4 - 4)!
= 4! / 0!
= 4! / 1
= 4 * 3 * 2 * 1
= 24
So, there are 24 different ways for the 4 people to line up to buy tickets at the Downtown Theater.