walker wrote:
\(p=\frac{12}{12}*\frac{10}{11}*\frac{8}{10}*\frac{6}{9}=\frac{16}{33}\)
or
\(p=\frac{C^6_4*(C^2_1)^4}{C^{12}_4}=\frac{16}{33}\)
or
\(p=\frac{P^6_4*(P^2_1)^4}{P^{12}_4}=\frac{16}{33}\)
Hi -- can someone please explain the reasoning for the last two equations? In the second equation, it stating the different ways 4 couples out of six can be selected(to give 4 individual people), followed by how many different ways to select 1 person out of the 2 people in a couple(and do it 4 times) and follow that by dividing the whole quantity by 12C4.
Can you explain WHY you're doing this?Same with the third equation -- what's different here now that we have 4P6 and not 6C4?
An additional question -- I've seen the equation
(12C1 * 10C1 * 8C1*6C1)/4!/ 12C4 -- why do we divide by 4! instead of multiply by 4!?