Probability

Question

in a game of bridge the  entire deck of 52 cards is dealt out to 4 players.What is the probability that

i)one of the players receive all 13 spades

ii )each player receives one ace?

Answer 1

The soln in my terms 

1) let there are 4 players A,B,C,D  

For player A 

First card a spade 13/52 second card also spade =12/51 and so on .... so 13x12x11x..1/(52x51x50...40)

and similarly for rest B,C,D so ans is 4 x(13 x12 x11....1) /(52x51x...40)

2)For player A  having exactly one ace   = 12 non ace and one ace at any location 12 non-ace=48x47x46x...37/52x51....41   one ace =4/40 =1/10  now ace can take any 13 position so 

prob of A  having exactly one ace =13 (48 x47x 46 x....37x4) /(52x51x50....41x40)

and same for B , C  ,D  so  

ans=  {13 (48 x47x 46 x....37x4) /(52x51x50....41x40)}⁴

for more details refer https://math.la.asu.edu/~quigg/teach/courses/421/2014fall/notes/stp421notes.pdf

Comments

Sir I understood the first part completely and it's absolutely correct.

But for the second part and given is ~= .1055