Question

What is the probability of getting 9 cards of the same suit in one hand at a game of bridge?

Answer 1

Answer:

4*¹³C₉*³⁹C₄/⁵²C₁₃

Step-by-step explanation:

Hi,

In a  game of bridge 13 cards are dealt t each of the 4 players

from a single deck of cards.

Total number of ways of getting 13 cards in  one hand are ⁵²C₁₃

To get 9 cards of the same suit, one can chose the particular

suit in 4 ways since there are 4 different suits and then 9 cards

to be dealt from that particular suit and the remaining 4 cards

should have been dealt from remaining 3 suites

So, 9 cards out of 13 cards of the same suit can be selected in

¹³C₉ ways and the remaining 4 cards out of 39 cards can be

selected in ³⁹C₄ ways and particular suite can be chosen in 4

different ways

Hence total number of selections are 4*¹³C₉*³⁹C₄

Hence the probability of getting 9 cards of same suit in one

hand are

= 4*¹³C₉*³⁹C₄/⁵²C₁₃

Hope, it helps !