Question

How to quickly calculate 5!/e

Answer 1

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

Answer 2

by hand

Answer 3

Do you mean pen and paper or mentally?

Answer 4

by pen and paper (hand)

Answer 5

So would that not be 120/2.718281828?

Answer 6

yes

Answer 7

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

Answer 8

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

Answer 9

it should be correct

Answer 10

Interesting problem. Will be back.

Answer 11

ur thinking is correct of \(\approx n/2.7\)

Answer 12

trying to learn derangements? :)

Answer 13

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.

Answer 14

nice forecasting of dearrangments.