Question

You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws. How many possible pairs of friends can be chosen this way?

Answer 1

Of the 6 friends, call them \(a,b,c,d,e,f\), you are selecting 2. It doesn't matter what the order is. What this means is that picking \(a\) then \(b\) is the same as picking \(b\) then \(a\). This means you're counting the number of combinations.
\[\binom62={}_6C_2=\frac{6!}{2!(6-2)!} \]