View Full Version : Inclusion - exclusion. Specific example

08-04-2005, 10:39 AM
Hi all,

My question is very specific and concerning an archived thread with BruceZ in the drivers seat:
http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=396447&page=&view=&sb=5&o =&fpart=1&vc=1

In Brucez's answer it follows:
" C(8,2)* 78/C(52,2) * 73/C(50,2) = 9.8%. C(8,2) is the number of ways to pick the 2 players. There are 73 pairs remaining after the first player chooses a pair"

- Now, why are there 73 pairs left after 1st player chooses a pair? I know we can't just pick from 12 ranks and pretend that the 2nd player can't pick a pair of the same rank as the first. But why 73...?

I want of course to be able to make the next term myself.


08-04-2005, 10:43 AM
Because there are 12 ranks remaining where there are 6 ways to choose a pocket pair...C(4,2), and one rank remaining where there's only one way to choose the pair (only two cards left). C(12,1) * C(4,2) + C(2,2) = 73.

08-04-2005, 10:59 AM
Ahhh. of course.