Answer
0.00069
Work Step by Step
For a hand, the order of cards is unimportant.
A (1234567) hand is the same as a (3124567) hand. We deal with combinations and use the combinations expression for the computation.
$P=\frac{\text { no. of hands that suit us }}{\text { total ways to choose a } 7 \text { card hand }} = \frac{8 C_{2} \cdot 25 C_{2} \cdot 25 C_{3}}{108 C_{7}}=\frac{\frac{8 !}{6 ! 2 !} \cdot \frac{25 !}{23 ! 2 !} \cdot \frac{25 !}{22 ! 3 !} }{\frac{108 !}{101 ! 7 !}}$
Hence, $P = 0.00069$
(Two cards out of eight possible wildcards.
Two out of 25 red cards. The rest three out of the 25 blue cards.
We choose 7 out of a total of 108 cards )
