Probability

 

Choose  5  cards  from  a deck of 52. There are  52C5  arrangement.

 

 

Probability of getting :

 

 

1.           Royal Flush              :           4 / 52C5 = 4 / 2598960

               (Straight Flush with A,K,Q,J,10)

 

 

2.           Straight Flush         :           (10 x 4 - 4) / 52C5 = 36 / 2598960

               (excluding Royal Flush)

 

 

3.           Four of a Kind         :           13 x 48 /52C5 = 624 / 2598960

 

 

4.           Full House                :           4C3 x 13 x 4C2 x 12 / 52C5 = 3744 / 2598960

 

 

5.           Flush                          :           (13C5 x 4 - 40) / 52C5  =  5108 / 2598960

 

 

6.           Straight                     :           (45 x 10 - 40) / 52C5  = 10200 / 2598960

 

 

7.           Three of a Kind        :           (4C3 x 13 x   48 x 44 / 2!) / 52C5  = 54912 / 2598960

 

 

8.           Two Pairs                 :           13C2 x 4C2 x 4C2 x 44 / 52C5  = 123552 / 2598960

 

 

9.           One Pair                   :           (13 x 4C2 x   48 x 44 x 40 / 3!) / 52C5  = 1098240 / 2598960

 

 

10.         Other                         :           1302540 /2598960