SOLUTION: How many different arrangements of four books on a shelf could you make from eight books?

You can choose the first book any of 8 ways,

For each of those 8 ways to choose the first book,
you can then choose the second book any of the 7 remaining ways.
That's 8×7 or 56 ways to choose the first two books.

For each of those 8×7 or 56 ways to choose the first two books,
you can then choose the third book any of the 6 remaining ways.
That's 8×7×6 or 336 ways to choose the first three books.

For each of those 8×7×6 or 336 ways to choose the first three books,
you can then choose the fourth book any of the 5 remaining ways.
That's 8×7×6×5 or 1680 ways to choose the four books.

Answer: 1680


This is a permutation problem since order of the books matters

That's the permutations of 8 things taken 4 at a time

On the TI-83 and 84 calculators, that's 8 nPr 4.

Here's how:

Press ON
Press CLEAR
Press 8
Press MATH
Press the left arrow key
Press 2
press 4
Press ENTER

You will see

8 nPr 4     
            1680

Edwin