The Downtown Theater has 1 ticket window. In how many ways can 4 people
line up to buy tickets?
4 choices for first place
3 for second place
2 for third place
1 for last place
4! = 4*3*2 = 24
To calculate the number of ways that 4 people can line up to buy tickets at the Downtown Theater's 1 ticket window, we can use the concept of permutations.
In this scenario, we want to find the number of arrangements in which the order matters. Each person can occupy one position in the line, and once a position is occupied, it cannot be occupied by another person.
The number of ways to arrange the 4 people can be determined using the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of objects (4 people) and r is the number of objects taken at a time (4).
Using this formula, we can calculate the number of ways as follows:
P(4, 4) = 4! / (4 - 4)!
= 4! / 0!
= 4 x 3 x 2 x 1 / 1
= 24 / 1
= 24
Therefore, there are 24 ways for the 4 people to line up and buy tickets at the Downtown Theater's 1 ticket window.
To find the number of ways 4 people can line up at the ticket window, we can use the concept of permutations.
In this case, since there is only one ticket window, the order in which the people line up matters. Therefore, we can find the number of permutations.
The formula to find the number of permutations is:
P(n, r) = n! / (n - r)!
Where:
- P(n, r) represents the number of permutations of n objects taken r at a time (in this case, people lining up at the ticket window).
- n! represents n factorial, which is the product of all positive integers less than or equal to n.
- (n - r)! represents the factorial of the difference between n and r.
In this case, n = 4 (4 people) and r = 4 (all 4 people are lining up).
Plugging these values into the formula:
P(4, 4) = 4! / (4 - 4)!
= 4! / 0!
= 4! / 1
= 4 * 3 * 2 * 1 / 1
= 24
Therefore, there are 24 different ways in which the 4 people can line up at the ticket window.