Answer:
24
Explanation:
In a standard deck, there are 4 suits. Therefore, there are:
• 4 cards numbered 3
,
• 4 Kings.
The number of ways we can select 3 out of the 4 cards labeled 3 is:
[tex]^4C_3[/tex]
The number of ways we can select 2 Kings out of the 4 Kings is:
[tex]^4C_2[/tex]
Therefore, the number of possible hands are:
[tex]\begin{gathered} \begin{aligned} & ^4C_3\times^4C_2=\frac{4 !}{(3 !)(1 !)}\frac{4 !}{(2 !)(2 !)}=\frac{4 \times3 !}{(3 !)(1 !)}\frac{4 \times3 \times2 !}{(2 !)(2 !)} \\ & =4\times\frac{4\times3}{2}\end{aligned} \\ =24 \end{gathered}[/tex]
There are 24 possible hands.
