#5**+5 **

In fact, there *is* a way to get the calculator here to calculate this (using the npr function):

$${\frac{{\left({\frac{{\mathtt{365}}{!}}{({\mathtt{365}}{\mathtt{\,-\,}}\left({\mathtt{365}}{\mathtt{\,-\,}}{\mathtt{335}}\right)){!}}}\right)}}{{{\mathtt{365}}}^{{\mathtt{30}}}}} = {\mathtt{0.293\: \!683\: \!757\: \!280\: \!731\: \!3}}$$

I entered the above as npr(365,(365-335))/365^30.

Alan
Aug 14, 2014

#1**0 **

Yep, way to large!

Basically, infinity/infinity^(365^30) which is extremely large.

((((infinity)/(infinity)))/73924080909700308571344669689235259082192300936032301233150064945220947265625)

AzizHusain
Aug 14, 2014

#2**+5 **

Notice that (365!/335!) =

(365*364*363*362..........338*337*336)

Note that there are 30 terms in the above.

And each one of these individual terms would be divided by 365.

So we would have

(365/365)*(364/365)*(363/365)*(362/365)........(338/365)*(337*365)*(336/365)

And note that the first term is 1, but all the rest of the terms are <1.

And the result of the last division (336/365) = .9205479452054795

And since this is being multiplied by all the preceding multiplications whose total product is < 1, we can say that the result of this expression is < 0.9205479452054795

(In fact, it's * far* less....)

I leave it to you to find the exact result......!!!!

CPhill
Aug 14, 2014

#3**0 **

Interesting explanation, Phill! So small, the calculator couldn't catch it!

AzizHusain
Aug 14, 2014

#5**+5 **

Best Answer

In fact, there *is* a way to get the calculator here to calculate this (using the npr function):

$${\frac{{\left({\frac{{\mathtt{365}}{!}}{({\mathtt{365}}{\mathtt{\,-\,}}\left({\mathtt{365}}{\mathtt{\,-\,}}{\mathtt{335}}\right)){!}}}\right)}}{{{\mathtt{365}}}^{{\mathtt{30}}}}} = {\mathtt{0.293\: \!683\: \!757\: \!280\: \!731\: \!3}}$$

I entered the above as npr(365,(365-335))/365^30.

Alan
Aug 14, 2014