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?