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Chapter 12: Problem 18

Six friends go to a movie theater. In how many different ways can they sit together in a row of 6 empty seats?

Short Answer

Expert verified
Therefore, the six friends can sit together in the movie theater in 720 different ways.

Step by step solution

01

Understanding Permutations

A permutation is a way to select items from a larger set where the order of the items matters. Since all the friends are distinct individuals and the seats they can sit in are unique positions (in this case 6), we are looking for the number of permutations of 6 items taken 6 at a time.
02

Calculating the Number of Permutations

The formula for calculating permutations is given by \(nPr = n! / (n-r)!\) where \(n\) is the number of total items, \(r\) is the number of items to choose, and \(!\) is the factorial operator meaning to multiply a series of descending natural numbers. Here \(n = r = 6\), so essentially we need to calculate \(6!\).
03

Evaluating the Factorial

To evaluate \(6!\), we need to multiply 6*5*4*3*2*1 which equals to 720.

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