using factorial in probability question

[resolved]

"The problem is you don't know that what you are asking is different then what you think you are asking!"

No doubt that is very true.... but in the mean time please explain why in HOME mode

365! / 252! I get 489.03... but
365! / 253! I get 0

I thought it might have to do with the calculator reaching it's limits, that is why searched for them

In CAS mode

365! / 252! I get undef
365! / 170! I get a huge number, I press a b/c and get +inf

In the CAS settings, the "Exact" is NOT checked --- by not checking the Exact option, doesn't this take the answer out of exact and put in decimal form???

In the CAS settings, Number Format is set to Scientific, yet the result is a string of numbers???