Five cards are drawn from a standard deck (not replaced). Determine the probability of drawing exactly 3 hearts and 2 diamonds.
The expression for the probability is:
$\frac{\binom{13}{3}\binom{13}{2}}{\binom{52}{5}}=\frac{143}{16660}$
Then, I used an another way to do it, by multiplying the probability of drawing the card at each draw.
$\overbrace{\frac{13}{52}\frac{12}{51}\frac{11}{50}}^{\mbox{hearts}} \overbrace{\frac{13}{49}\frac{12}{48}}^{\mbox{diamonds}}$
Then the math teacher corrected me, she added the the number of permutations of 5 cards of that type.
$\frac{13}{52}\frac{12}{51}\frac{11}{50} \frac{13}{49}\frac{12}{48}(\frac{5!}{3!2!})$
I don't know why that term for number of permutations is required for that expression, and why that works.