Sheldon Ross example 5h

Question

In the game of bridge, the entire deck of 52 cards is dealt out to 4 players. What is the
probability that
(a) one of the players receives all 13 spades;
(b) each player receives 1 ace?

Comments

well first part is easy a) 4/52C13

If A,B,C,D are 4 player

A can get spade 13C13 or B can get spade 13C13 ...  this gives 1+1+1+1 = 4 then probability becomes 4/52C13

b) https://socratic.org/questions/in-a-bridge-game-of-playing-cards-4-players-are-distributed-one-card-each-by-tur

you will get idea from here.

 

---

1)$\frac{1}{\binom{52}{13}}$

2)$\frac{4!}{\binom{52}{4}}$

---

@srestha we are considering group of 4 players, your first answer is valid if there would have been only 1 player. in b part we need to consider other combinations as well.

This can also be solved using multinomial coefficients

If there are n distinct objects to be placed in r groups having group size of n1,n2,.... then it can be done in

$\frac{n!}{n1!n2!n3!...nr!}$

---

Thanks @Swapnil Naik brother....nicely explained!