How many different ways can six friends stand in line at the movies if Alice and David refuse to stand next to each other

Step-by-step explanation:

Let the other 4 friends arrange themselves first. There are 4! ways to do so.

Now there are 3 spaces between the 4 friends, and 1 at each end (total 5 spaces)

Example: _F_F_F_F_

Alice can choose to stand in any of the 5 spaces. David can choose to stand in any of the 4 remaining spaces (now Alice and David are not next to each other)

Total number of ways = 4! * 5 * 4 = 480.

40 minutes

step-by-step explanation:

add the time and multiply by 2