A urn contains blue balls and red balls. I need to find probabiltiy of drawing more blue balls than red balls 
A urn contains 5 identical blue balls and 4 identical red balls. Taking 5 balls at random from the urn what is the probability that the number of blue balls be greater than the number of red balls? 

My first guess was setting the ways that I can draw the balls.
It was:

$\color{blue} {BBBBB}$ ; $\color{blue} {BBBB}\color{red}{R}$; $\color{blue} {BBB}\color{red}{RR}$; $\color{blue} {BB}\color{red}{RRR}$; $\color{blue} {B}\color{red}{RRRR}$

Only $3$ cases have the number of blue balls greater than the number of red balls. Then the odds must be $\displaystyle{\frac{3}{5}}$.
But this answer sounds strange for me. I think that it is wrong?
Could anyone help me how to figure out this question?

Hint
There are $31$ permutations for selecting $5$ balls:
$$\left(
\begin{array}{ccccc}
 \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} \\
 \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} \\
 \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} \\
 \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{red}{R} \\
 \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} \\
 \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{red}{R} \\
 \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{blue}{B} \\
 \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{red}{R} \\
 \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} \\
 \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} \\
 \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} \\
 \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{red}{R} \\
 \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} \\
 \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{red}{R} \\
 \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{red}{R} & \color{blue}{B} \\
 \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{red}{R} & \color{red}{R} \\
 \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} \\
 \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} \\
 \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} \\
 \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} & \color{red}{R} \\
 \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} \\
 \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} & \color{red}{R} \\
 \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{blue}{B} \\
 \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{red}{R} & \color{red}{R} \\
 \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{blue}{B} \\
 \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} & \color{red}{R} \\
 \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{blue}{B} \\
 \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{red}{R} & \color{red}{R} \\
 \color{red}{R} & \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{blue}{B} \\
 \color{red}{R} & \color{red}{R} & \color{red}{R} & \color{blue}{B} & \color{red}{R} \\
 \color{red}{R} & \color{red}{R} & \color{red}{R} & \color{red}{R} & \color{blue}{B} \\
\end {array}
\right)$$
(Was too long to post as a comment, my apologies)
