$\color{#D61F06}{Colourful}$ Probability

A bag contains $6$ $\color{#D61F06} {\text{red}}$ and $3$ ${\text{white}}$ balls.Four balls are drawn out randomly one by one and are not replaced.What is the probability that they are alternatively of different colours?

$\textbf{Details and Assumptions}$

One such sequence may be: $\color{#D61F06} {\textbf{red}}$,${\textbf{white}}$,$\color{#D61F06} {\textbf{red}}$,${\textbf{white}}$

If the probability can be expressed in the form $\dfrac{a}{b}$where $a$ and $b$ are co prime integers then find $a+b$