I've tried to solve the following problem: In how many ways can you choose 3 pairs from a group of 50 persons?
My attempt:
You first have a group of 50 persons to choose from, you want to take 2 elements from the group of 50 (50 choose 2) and then you have a group of 48 of which you choose 2 (48 choose 2) and so on. The multiplication principle gives you the following since all of these are dependent scenarios.
$\binom{50}{2}*\binom{48}{2}*\binom{46}{2}$=1548078480
Is this correct? Thanks beforehand
$\endgroup$ 11 Answer
$\begingroup$The answer should be
$$\binom{50}{2}\binom{48}{2}\binom{46}{2}\div 3!=238360500$$
Choosing $(A,B),(C,D),(E,F)$ is the same as $(C,D),(E,F),(A,B)$, etc.
$\endgroup$ 1
