Question

A fair die is cast seven times to obtain a sequence of seven numbers. How many sequences have the property that each of the 6 possible values occurs at least once?

Answer 1

One way I can think to approach this is:
If you need a sequence of 7 numbers, and all 6 possible values have to occur at least once, then, you can have the following situations:
1) How many ways can you arrange \(123456\color{red}{1}\)
2) How many ways can you arrange \(123456\color{red}{2}\)
3) How many ways can you arrange \(123456\color{red}{3}\)
4) How many ways can you arrange \(123456\color{red}{4}\)
5) How many ways can you arrange \(123456\color{red}{5}\)
6) How many ways can you arrange \(123456\color{red}{6}\)

And add all the arrangement possibilities from 1) to 6) to get the total number of sequences

Answer 2

Thank you.

Answer 3

:)