The probability of getting 9 cards of the same suit in one hand at a game of bridge is:
4 × ¹³C₉ × ³⁹C₄ / ⁵²C₁₃
Total hands: 13 cards chosen from 52, i.e. \(\binom{52}{13}\).
Favourable hands (exactly 9 of one suit):
Choose the suit in \(\binom{4}{1}=4\) ways, pick 9 of its 13 cards in \(\binom{13}{9}\) ways, and fill the remaining 4 cards from the other 39 cards in \(\binom{39}{4}\) ways.
\[P = \dfrac{4 \times \binom{13}{9} \times \binom{39}{4}}{\binom{52}{13}}\]
This matches option (1).
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