I am having trouble finding the number of flushes in a deck of 52 cards. My logic is that you have 52 choices for the first card, 12 choices for the second, 11 for the third, etc. The number of flushes should thus be equal to:
$$52 \cdot 12 \cdot 11 \cdot 10 \cdot 9 = 617760$$
How is this logic incorrect?