A certain number of friends are waiting in line to board a new roller coaster. they can board the ride in 5,040 different ways. How many friends are in line?

Question

Mathematics

Vaughn Wilkinson

4 November, 00:15

A certain number of friends are waiting in line to board a new roller coaster. they can board the ride in 5,040 different ways. How many friends are in line?

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Answers (1)

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Brian Lamb · Answer 1

There are seven (7) friends.

The first friend to board can be any one of the 7. For each of them ...

The 2nd one to board can be any one of the remaining 6. For each of them ...

The 3rd one to board can be any one of the remaining 5. For each of them ...

The 4th one to board can be any one of the remaining 4. For each of them ...

The 5th one to board can be any one of the remaining 3. For each of them ...

The 6th one to board can be either of the remaining 2. For each of them ...

The 7th one to board is the last 1 standing.

The number of different ways that this could play out is

(7 x 6 x 5 x 4 x 3 x 2 x 1) = 5,040