The numbers from 1 to 11 are drawn at random. Find the probability that the even numbers will all be drawn before the odd numbers.

We have 5 even numbers

We can choose any 5 of the even numbers first.....

And then any 4

And then any 3

And then any 2

And then the last

So....the probability is

(5/11) (4/10) (3/9) ( 2/8) (1/7)  =

(5/11) (2/5) (1/3)(1/4)(1/7)  =

10 / 4620    =   1 / 462

Another way of looking at this is to note that we have 5! ways of arranging the even digits first and 6! ways of arranging the odd digits second

And the total possible arrangements =  11!

So....the probability is  

5! * 6!  / 11!    =    1 / 462