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 ?
This is combinatorics related question. We need to find how many different groups we can make. To find this we use formula: [tex]n={N\choose k}[/tex] Where: n=number of groups N=number of people to choose from k=number of people that we choose
In our case we have: [tex]n={5\choose 3}[/tex]
To calculate this we use binomial formula: [tex]n= \frac{N!}{(N-k)!*k!} \\ \\ n= \frac{5!}{2!*3!} \\ \\ n= \frac{120}{2*6} \\ \\ n= \frac{120}{12} \\ \\ n=10[/tex]
