Question

In how many ways you can put 20 books on 50 shelves so that there is not more than one book on a shelf?

Answer 1

9514 1404 393

Answer:

• 47129212243960 ≈ 4.713×10^13 if order doesn't matter
• 114660755112113373922453094400000 ≈ 1.147×10^32 if it does

Explanation:

If order doesn't matter, the number is the combinations of 50 things taken 20 at a time:

50C20 = 47129212243960 ≈ 4.713×10^13

If order does matter, then the number of ways is this value multiplied by 20!:

50P20 = 114660755112113373922453094400000 ≈ 1.147×10^32

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nCk = n!/(k!(n-k)!)

nPk = n!/(n-k)!