We have 6 people, A,B,C,D,E,F in a committee and we're to select a chair, secretary and a treasurer. In how many ways can this be done?
My initial attempt was: Ok easy, we just count how many ways we can select 3 people from 6, since obviously, we will assign these three selected people to the different roles, and we don't care about the order. Sounds simple right? Just $C(6,3)$.
That's wrong however and I yet again don't undersand why. (I understand why it's $6\times5\times4$ but why not $C(6,3)$?)
Your answer is almost correct. However, once the three people are chosen in ${6 \choose 3}$ ways, they need to be assigned 3 different roles. This can be done in $3!$ ways. Thus, the final answer comes to ${6\choose3}3!=120$