SOLUTION: Five boxes are to be arranged on a shelf, but there is only enough space for three books. In how many ways can these books be arranged on the shelf?

Question 1105467: Five boxes are to be arranged on a shelf, but there is only enough space for three books. In how many ways can these books be arranged on the shelf?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

I think you meant to write "books" instead of "boxes".

We have five books but only enough space for three of them.

Label the three empty spaces as
Slot A
Slot B
Slot C

There are 5 choices for slot A.
After you've picked a book to go into slot A, there are 5-1 = 4 choices for slot B since you cannot have a book occupy more than one slot at a time.
For slot C, there are 3 choices left.

So have 5*4*3 = 20*3 = 60 different permutations.

If you wish to use a formula, then you can use the nPr formula
nPr = (n!)/(n-r)!
where you plug in n = 5 and r = 3 to get the same result of 60

Answer: 60

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