Question

You just got a free ticket for a boat ride, and you can bring along 3 friends! Unfortunately,you have 5 friends who want to come along.

How many different groups of friends could you take with you ?

Answer 1

This is combinatorics related question. We need to find how many different groups we can make. To find this we use formula:

`n={N\choose k}`
Where:
n=number of groups
N=number of people to choose from
k=number of people that we choose

In our case we have:

`n={5\choose 3}`

To calculate this we use binomial formula:

`n= (N!)/((N-k)!*k!) \\ \\ n= (5!)/(2!*3!) \\ \\ n= (120)/(2*6) \\ \\ n= (120)/(12) \\ \\ n=10`

We can make 10 different groups.