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Chapter 11: Problem 68

Ten people board an airplane that has 12 aisle seats. In how many ways can they be seated if they all select aisle seats?

Short Answer

Expert verified
So, the ten people can be seated in 239,500,800 different ways if they all choose aisle seats.

Step by step solution

01

Understanding the Problem

There are 12 aisle seats and 10 people who want to select those seats. This is a case of permutation where order matters, because person A sitting in seat 1 and person B in seat 2 is a different arrangement from person B in seat 1 and person A in seat 2.
02

Apply the Permutation formula for counting

The formula for permutation is nPr = n!/(n-r)!, where n is the total number of items, and r is the number of items to choose. In this case, n = 12 (aisle seats) and r = 10 (people).
03

Calculation

Substituting the values into the formula, we get 12P10 = 12!/2!
04

Calculate the Factorial Values

We calculate each factorial and insert the values back into the formula. 12! (factorial) is 479001600 and 2! is 2. So, 12P10 = 479001600/2 = 239500800.

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