Question 1120971

<pre>The numerator of the desired probability is the number of ways
to choose two blues and two reds:
5 blue marbles choose 2 in 5C2 = (5&#8729;4)/(2&#8729;1) = 20/2 = 10 ways.
2 red marbles choose 2 in 2C2 = (2&#8729;1)/(2&#8729;1) = 2/2 = 1 way.

So the number of ways to choose 2 blues and 2 reds is:
(5C2)(2C2) = 10&#8729;1 = 10 ways. 

So the numerator of the desired probability is 10.

The denominator of the desired probability is the number of ways
to choose ANY 4 marbles:

4+5+2+3 = 14 marbles choose 4 = 14C4 = (14&#8729;13&#8729;12&#8729;11)/(4&#8729;3&#8729;2&#8729;1) = 24024/24 = 1001 ways.

So the denominator of the desired probability is 1001.

The desired probability is therefore 10/1001. 

Edwin</pre>