Question

WILL MEDAL!!!!

A television director is scheduling a certain sponsor's commercials for an upcoming broadcast. There are six slots available for commercials. In how many ways may these same people line up if two of the people refuse to stand next to each other?

Answer 1

@agent0smith @Michele_Laino @jhonyy9 @mathstudent55

Answer 2

@jhonyy9

Answer 3

How many people are there?

Answer 4

5 people

Answer 5

@tacotime

Answer 6

So I think the total number is the number of slots * the number of people ie 6 * 5 which is 30 but you have to subtract the number of ways A and B can be together. If you draw all the situations out (eg AB____ and _AB___, etc.) You can get 20 different possibilities so subtract 20 from 30 to get 10.

Answer 7

The answer key says that the way to do this is:
\(\large 5! - 4 \times 3 \times 2! = 72\)

Problem is, I don't know how they got this equation to evaluate to find the answer.