Colourful\color{Red}{Colourful} Probability

A bag contains 66 red\color{Red} {\text{red}} and 33 white{\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?

Details and Assumptions\textbf{Details and Assumptions}

One such sequence may be: red\color{Red} {\textbf{red}},white{\textbf{white}},red\color{Red} {\textbf{red}},white{\textbf{white}}

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

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