In how many ways can five people sit next to each other in a theater row

120 ways

Step-by-step explanation:

This is a problem of combination.

We will solve this in steps.

First person : He has 5 ways to be seated in the row.

Second person : He has 4 ways to be seated in the row as one seat is already occupied now.

Third person : He has 3 ways to be seated in the row as two seats are already occupied now.

Forth person : He has 2 ways to be seated in the row as three seats are already occupied now.

Fifth person : He has only 1 place to sit in the row as four seats are already occupied now.

Hence total number of ways = 5 x 4 x 3 x 2 x 1 = 120

Hence there are 120 ways for five people to be seated together in a row