On probabilities, the order is what makes students more confused... And I got some doubts that I would like to discuss with you.
I got a group of 5 dices and 6 distinct numbers. It I want 2 groups of 2 dices with the same number (2 pairs), I can do it
$$\binom 52\binom 32\binom 11\binom 62\binom 41$$
Since the 2 pairs are multiplying each other, they are permuting, and then I distribute 2 numbers from 6 to these pairs.
My question is about the full house! (1 pair, 1 triplet) My way of doing it is incorrect:
$$\binom 52\binom 22\binom 62$$
If in the anterior case, I am considering the order, since I am 2 pairs of the same "bag" of dices, why in this case I am not permuting the pair with the triplet?
Thanks