Answer
Probability = $\frac{123552}{2398960}$ $\approx$ 0.0476
Work Step by Step
Number of ways to select 5 cards from deck = $C$(52,5) = 2598960
Ways to select 2 pairs
- First we select any 2 denomination out of 13 i.e. $C$(13,2) = 78
- Pair can have any 2 suits out of 4 i.e. $C$(4,2) = 6
= $C$(13,2)$\times$$C$(4,2)$\times$$C$(4,2) = 78$\times$6$\times$6 = 2808
Ways to select last card = $C$(44,1) = 44 [card should not have the same denomination as the 2 pair]
Ways to select 2 pairs in 5 cards = 2808$\times$44 = 123552
Probability = $\frac{123552}{2398960}$ $\approx$ 0.0476
