He have a deck with $52$ cards and $4$ suits, $H$,$D$,$C$,$S$, from which you take $26$ cards.
There are some combinations that, when taken with the same suit, give a prize.
Let's those combinations be: $(A,2,3,4,5)$, $(A,3,5,7,9,J,K)$; and no other of the same suit), $(not A, 2, 3, 4, 6)$, $(J, Q, K)$.
What's the probability of winning at least one prize?
Furthermore, would you be able to find a way to calculate the same on a computer (so using an algorithm that doesn't take eons to finish) when the number of possible combinations is way bigger?