Question 649593
N[at least one club]  = N[total ways] - N'[at least one club] = N[total ways] - N[no clubs]

There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.

There are 2598960 possible hands, leaving us with 2598960-575757 ways.

Which is 2023203 hands.