how many different ways to hit 21

[Three]

Noted Gronbog. I was merely pointing out to T3 that I see 4 different 3 card combinations for 7's, not 1 in a single deck. To which T3 must surely concur.

For most things card suits are irrelevant in the casino. There are exceptions. Unless otherwise stated I assume ranks are suitless when asked a question. But if you want to consider suit there are 48 different ways to get 777.
7c, 7c, 7c
7c, 7c, 7d
7c, 7c, 7h
7c, 7c, 7s
7c, 7d, 7c
7c, 7d, 7d
7c, 7d, 7h
7c, 7d, 7s
7c, 7h, 7c
7c, 7h, 7d
7c, 7h, 7h
7c, 7h, 7s
7c, 7s, 7c
7c, 7s, 7d
7c, 7s, 7h
7c, 7s, 7s

7d, 7c, 7c
7d, 7c, 7d
7d, 7c, 7h
7d, 7c, 7s
7d, 7d, 7c
7d, 7d, 7d
7d, 7d, 7h
7d, 7d, 7s
7d, 7h, 7c
7d, 7h, 7d
7d, 7h, 7h
7d, 7h, 7s
7d, 7s, 7c
7d, 7s, 7d
7d, 7s, 7h
7d, 7s, 7s

7h, 7c, 7c
7h, 7c, 7d
7h, 7c, 7h
7h, 7c, 7s
7h, 7d, 7c
7h, 7d, 7d
7h, 7d, 7h
7h, 7d, 7s
7h, 7h, 7c
7h, 7h, 7d
7h, 7h, 7h
7h, 7h, 7s
7h, 7s, 7c
7h, 7s, 7d
7h, 7s, 7h
7h, 7s, 7s

7s, 7c, 7c
7s, 7c, 7d
7s, 7c, 7h
7s, 7c, 7s
7s, 7d, 7c
7s, 7d, 7d
7s, 7d, 7h
7s, 7d, 7s
7s, 7h, 7c
7s, 7h, 7d
7s, 7h, 7h
7s, 7h, 7s
7s, 7s, 7c
7s, 7s, 7d
7s, 7s, 7h
7s, 7s, 7s