Question

A six card hand is dealt from a standard 52 card deck. What is the probability of obtaining two pairs

Answer 1

This can be solved using combination

Part a

No of combination to draw 6 cards

⁵²C₆ =    

=

= 20358520   ….(A)

Part b

For Two Pairs

• For two pairs we have ¹³C₂ choices
• For each pair to be selected we have ⁴C₂ choices
• For other two cards we have ¹¹C₂ choices
• Each of 2 cards can be selected from 4 types of cards

So

                = (¹³C₂)*(⁴C₂)²*(¹¹C₂)*(⁴C₁)²

                = 78*36*55*16 = 2471040 … (B)

So required probability =B/A

                =

= 0.12137621 Ans