## mathmath333 one year ago How to quickly calculate 5!/e

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ How to quickly calculate}\hspace{.33em}\\~\\ & \lfloor{\dfrac{5!}{e}\rfloor} \hspace{.33em}\\~\\ \end{align}}

2. mathmath333

by hand

3. mathmate

Do you mean pen and paper or mentally?

4. mathmath333

by pen and paper (hand)

5. mathmate

So would that not be 120/2.718281828?

6. mathmath333

yes

7. mathmate

Or you can do a quick mental approximation by 120/2.7=40/0.9=44.4

8. mathmate

If you want to refine it, subtract 2/300 of the calculated value (mentally if you want) to get 44.15 Accurate value is 44.14553294057308

9. mathmath333

it should be correct

10. mathmate

Interesting problem. Will be back.

11. mathmath333

ur thinking is correct of $$\approx n/2.7$$

12. anonymous

trying to learn derangements? :)

13. mathmate

As long as it is between 44 and 45, the floor function will convert it to 44. We need additional accuracy to get the lower bound so it doesn't go below 44.

14. mathmath333

nice forecasting of dearrangments.