I tried these homework problems but think I ended up double counting on a few. I will post the question followed by my answer. I need help checking that they are correct or what the answer really is.
Consider a game where 4 cards are dealt from a standard 52 card deck. Determine the number of hands that contain:
(a) 4 different suits
$13C1^4 \cdot 4C1 \cdot 3C1 \cdot 2C1 \cdot 1C1 = 685,464$
(b) 4 different suits and 4 different weights
$13C1 \cdot 4C1 \cdot 12C1 \cdot 3C1 \cdot 11C1 \cdot 2C1 \cdot 10C1 \cdot 1C1 = 411,840$
(c) 4 consecutive ranks
$11C1 \cdot 4C1^4 = 2816$