Question

A family of five is taking an extended vacation. Every day at lunch they stand in line at a cafeteria in a different order than ever before. On the last day, however, they can't help repeating a previous order. Their vacation lasted

Answer 1

Their vacation lasted 121 days.

Explanation:

Consider the provided information.

A family of five is taking an extended vacation. Every day at lunch they stand in line at a cafeteria in a different order than ever before.

Therefore, the number of possible ways are:
`5!`

`5!=5* 4* 3 * 2* 1=120`

On the last day, however, they can't help repeating a previous order.

That means on the last day they repeat the previous order.

Therefore the total number of ways are:
`120+1=121`

Hence, their vacation lasted 121 days.