Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 15 people can line up in a row for concert tickets.
Does the situation involve permutations, combinations, or neither? Choose the correct answer below.
A. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.
B. Combinations. The order of the 15 people in line does not matter.
C. Permutations. The order of the 15 people in line matters.
Final Answer: The correct answer is Permutations. The order of the 15 people in line matters. The number of ways 15 people can line up in a row for concert tickets is \(\boxed{1307674368000}\).
Step 1 :Decide if the situation involves permutations, combinations, or neither. The question is asking for the number of ways 15 people can line up in a row for concert tickets. This implies that the order in which the people are arranged matters. For example, if person A is first in line and person B is second, that's a different arrangement than if person B is first and person A is second. Therefore, this situation involves permutations, not combinations or neither.
Step 2 :The number of ways 15 people can line up in a row for concert tickets is calculated as the factorial of the number of people, which is 15. The factorial of a number is the product of all positive integers less than or equal to that number. In this case, the factorial of 15 is 1307674368000.
Step 3 :Final Answer: The correct answer is Permutations. The order of the 15 people in line matters. The number of ways 15 people can line up in a row for concert tickets is \(\boxed{1307674368000}\).