Question

Find the number of possibilities in each scenario. A group of 16 people need to take an elevator to the top floor. They will go in groups of eight. They are deciding who will take the elevator on its second trip.

A. 56 possibilities
B. 28 possibilities
C. 16 possibilities
D. 8 possibilities

Answer 1

The number of possibilities for who will take the elevator on its second trip is calculated using the combination formula, where 16 people are choosing 8 to ride the elevator.

Step-by-step explanation:

To find the number of possibilities for who will take the elevator on its second trip, we need to calculate the number of combinations of 8 people who can be selected from the 16 people.

This can be calculated using the combination formula, which is written as:

C(n, k) = n! / [k! * (n-k)!]

where:

• n = total number of people
• k = number of people in each group
• n! = factorial of n
• k! = factorial of k

In this scenario, n = 16 (total number of people) and k = 8 (size of group for the elevator ride). Therefore, the combination will be:

C(16, 8) = 16! / [8! * (16-8)!]