In a standard deck of $52$ cards, what is the minimum number of cards you need to pick up, in order to guarantee that there is a suit with at least $3$ cards?
Shouldn't I pick $10$ cards? Please explain in detail.
Also, what would be the minimum number of cards to be drawn out such that a suit has at most $3$ cards in the LEFT-UP pile?
Turn the question around: what’s the most cards you can pick up without getting $3$ in one suit? There are $4$ suits, so if you have at most $2$ cards in each of them, you can have at most $4\cdot2=8$ cards. The moment you pick a ninth card, you must have at least one suit with at least $3$ cards in it.