# How to approach selecting a sample of three people from a group of six?

I'm currently studying introductory statistics, and I'm having a difficult time intuitively understanding the approach here.

In my textbook, it says: "Selecting a sample of three persons from a group of six people to form a committee of three people results in the choice of 20 committees." This is because "6 choose 3" equals 20.

But next it says, "If we were instead to select a treasurer, a captain, and a typist out of the group of six, we would have a total of 6 x 5 x 4 = 120 outcomes."

I am having a hard time understanding why these are two different problems. Aren't they both asking to choose three people from a list of six? Does it have to do with order, or replacement?

• @SwordSaintAshina Incidentally you might notice that 120 = 20 * 6; once you have selected a team of 3, there are 6 different ways to assign these 3 people to the 3 posts Treasurer, Captain and Typist. Generally, the number of ways to assign k people to k posts out of n people is (n choose k) * n!. – Stef Oct 29 at 14:09