Question

Directions: Each of the following sets are similar real-life situations. Solve these problems accurately using the appropriate combinatorics.

1. You are tasked to take pictures of Dan, Ben, Yla, Jun, and May taking three of them at a time. How many possible ways can you photograph them completely?

2. You are tasked to choose three of your classmates from Dan, Ben, Yla, Jun, and May to be your group mates. How many possible groups will you have?

please my Question}:‑)​

Answer 1

[1] 60 possible ways

There are 5 people with 3 "spots."

We can use the following formula to solve for the possible ways that they could be photographed. This calls for a "permutation."

-> n is the total number of people, 5

-> r is the sample, 3, we are taking a picture of at a time

n! / (n−r)!

5! / (5−3)!

5! / (2)!

120 / 2

60

[2] 10 different groups

There are 5 people with 3 "spots."

We can use the following formula to solve for the possible combinations your group mates could end up being. This calls for a "combination."

-> n is the total number of people, 5

-> r is the sample, 3, we are taking 3 people to be a part of our group at a time

n! / (r!(n−r)!)

5! / (3!(5−3)!)

5! / (3!(2)!)

5! / (3!(2)!)

120 / 12

10