Question 1208649
.
<pre>

We choose 2 kings from 4 kings in  {{{C[4]^2}}} = {{{(4*3)/2}}} = 6 different ways.

We choose 3 queens from 4 queens in  {{{C[4]^3}}} = 4 different ways.

We choose (7-2-3) = 2 another cards from the pool of 52-4-4 = 44 another cards 
in  {{{C[44]^2}}} = {{{(44*43)/2}}} = 22*43 = 946 different ways.


Thus the total number of different choices is  6*4*946 = 22704.    <U>ANSWER</U>
</pre>

Solved.