Excellent. Thanks. Let me see if I understand. Say the game ends in 7 rounds. The possible outcomes are:
$$25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19$$
One way to make this happen is to draw 1-1-1-2-3-4-5, which gets us:
$$25 \cdot 4 \cdot 3 \cdot 20 \cdot 15 \cdot 10 \cdot 5$$...
A deck of 25 cards consists of 5 suits, 5 cards of each suit, no other values. Cards are face down and randomized, and revealed one at a time. The only other rule is that the game ends when at least one card of each suit is revealed (meaning, at most 21 cards will be revealed).
I'm trying...