In how many ways can five airplanes line up for departure on a ru...

Question

In how many ways can five airplanes line up for departure on a runway?

Accepted Answer

Welcome back. I'm so glad you're here. We've got seven people lined up in a Q. And a cafeteria. I wonder if they've got sloppy joes or what? And how many ways can they line up? Okay. The first question here does order matter. Does it matter what order these people are standing in? It does someone's standing in the first spot in the second spot in the third spot and so on. So yes order matters. And that means we're dealing with permutation. We can write permutation notation where we've got n. Things taken are at a time end things. How many things do we have? Seven customers? Seven people. So N is seven. And how many of those things? How many of those people are we taking at a time? We're taking all seven at once. So R. Is also seven in this case we were called from previous lessons that and things taken R. At a time. The formula for permutation is N. Factorial over parentheses, N minus R. And parentheses factorial. Now we can just fill that in. We've got N is seven. So seven factorial over parentheses, N is seven minus R. Is seven. And parentheses factorial simplifying on the top still seven factorial on the bottom seven minus seven is 00 factorial. If you recall from previous lessons that zero factorial equals one. Now if you've got a calculator that can do factorial just type that in. You'll get your answer. If not you can always type in seven times six times five times four times three times two times one You don't have to divide it by one because that will just be itself. But that will give us an answer of 5040. Can you believe that those seven people can line up over different ways? That blows my mind. That matches with answer choice? A well done, we'll catch you on the next one.

In how many ways can five airplanes line up for departure on a runway?

Key Concepts

Permutations

Factorial

Combinatorial Counting

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