In shuffling a standard deck, three cards are accidentally dropped. What is the probability that the three missing cards are all of different suits?

Introduction / Context:
We draw 3 cards from 52 without order. We want all three to come from three distinct suits. Counting can be done by choosing suits first and then one card from each suit.

Given Data / Assumptions:

• Standard deck: 4 suits, 13 cards per suit.
• Drawn cards are unordered (combinations).

Concept / Approach:
Favorable outcomes: choose 3 suits out of 4 (C(4,3)) and choose 1 card from each chosen suit (13 choices independently per suit). Total outcomes: choose any 3 cards (C(52,3)). The ratio gives the probability.

Step-by-Step Solution:

Verification / Alternative check:
Reduction: 8788/22100 divide numerator and denominator by 52? Instead, observe 8788 = 413^3 and 22100 = 42552; simplifying yields 169/425 exactly.

Why Other Options Are Wrong:
261/425 and 104/425 correspond to different suit-pattern counts (allowing repetitions); “None of these” is unnecessary as the exact simplified fraction is available.

Common Pitfalls:
Overcounting by permuting the three cards even though combinations are used; or forcing an order among suits (unnecessary), which would multiply by 3! incorrectly.

Final Answer:
169/425