Math Help - BiNomial Distribution Formula

1. BiNomial Distribution Formula

My question is in regards to the binomial distribution formula:
Here is the formula...

it seems to work perfectly when finiding the probability of Exactly 10 customers.

The problem I am having is I can use online Binomial calculators and get the answer.. but i was wondering what formula to use if you are trying to find the probability of for example X > 1 , X < 3

stuff where its not exactly X = 10 or X = 1....

Any help would be greatly appreciated.

2. Hey !

$10!*10! {\color{red}\neq} 100! {\color{red}\neq} 20!*5!$
Don't try to simplify this way, it won't work.

As for finding P(X>1), think that it is the complementary of $P(X\leq 1)=P(X=1)+P(X=0)$

Same for $P(X>3)$

and this is the problem of the binomial distribution, when you have to calculate let's say P(X<10), you have to compute the sum $\sum_{k=0}^9 P(X=k)$