I often use this example, last night given as homework: if you have a bottle of bourbon, one of scotch, and another of beer, how many ways can you pour a tasting? The order in which you drink the spirits and the fruit of the barely will affect the taste of each. Start with the scotch and the beer will taste differently than if you had started with the beer. And so on.
There are three choices for the first drink. Once that is chosen, there are two choices for the second. And once that is imbibed, there is only one choice left. That makes 3 x 2 x 1 = 6 arrangements, which has the special mathematical name 3!, read “3 factorial.”
Now add in the mix Count Balboa (or similarly named), a Spanish rioja. There are now four choices for the first drink; after that three choices for the second, and so on. Answer: 4! = 4 x 3 x 2 x 1 = 24 arrangements.
Since by now we’re getting good at this, enter into the lists a syrupy Chardonnay, imported from some vague Eastern European country. Then, for good measure, include a by-now rapidly warming rosé produced at a Finger Lakes winery.
And since we’re on a roll, we might as well include a red wine with an unreadable label given as a gift for client services, and then another bottle, which by this time is the most delicious red you have ever tasted in your life. Of course, we mustn’t forget—we must never forget—Jameson’s, a splendid Irish whiskey.
How many choices now, huh? Huh?
I don’t care. See you tomorrow.