Question

How many ways can five​ people, A,​ B, C,​ D, and​ E, sit in a row at a movie theater if D and E will not sit next to each​ other?

Answer 1

Answer:

The total number of ways in which the 5 people can sit is: 5!=120: 5!=120

Let us assume that person d and e are sitting together and are taken as a single entity, the number of ways in which 4 people can sit is: 4!=24: 4!=24

The number of ways in which d and e are not sitting together: 1120−24=96.