# Math Help - Probability- Inclusion Exclusion rule

1. ## Probability- Inclusion Exclusion rule

Hi all,

In a drawing, six DISTINCT numbers are chosen at random from 1,2,...45. What is the probability that not all of the numbers 1,2,...45 will come up in 30 drawings?

I'm trying to use the inclusion exclusion rule. So, I define A_i as the event that number i does not get chosen in one drawing. This would be equal to (43*42*41*40*39*39)/(45*44*43*42*41*40) = 13/15

This is the probability given to any number, and so P(A_1 U A_2 U A_3 U ... U A_45) = 45 * (13/15) - inclusion exclusion stuff. But this seems off as 45 * (13/15) is a huge number.

Any help?

Thanks

2. ## Re: Probability- Inclusion Exclusion rule

Hey sfspitfire23.