Calculating Probability of Extracting 5 Pairs of Different Colored Balls

[etf]

Hi!
Here is my task:
There are 5 white and 5 black balls in box. Two balls at the time are extracted from box. Let random variable X be "number of extractions of balls with same colour. Find probability of random variable.

x can go from 0 (5 times we extract two by two balls and they are with different colour) to 5 (5 times we extract two by two balls and they are with same colour). I started with P(x=0) and I stucked there. How to calculate number of all possible events when extracting two by two balls at the time and number of all possible events of interest (we extract 5 pairs of balls and they are with different colours)?
Few events of interest woul be for example:
black ball white ball, black ball white ball, black ball white ball, black ball white ball,black ball white ball or
white ball black ball, white ball black ball, white ball black ball, white ball black ball, white ball black ball or
white ball black ball, black ball white ball, black ball white ball, black ball white ball, white ball black ball
etc.

 

[etf]

Result is:
$$X: \begin{pmatrix}
0 & 2 & 4 \\
8/63 & 40/63 &15/63
\end{pmatrix} $$

 

[Ray Vickson]

Hi!
Here is my task:
There are 5 white and 5 black balls in box. Two balls at the time are extracted from box. Let random variable X be "number of extractions of balls with same colour. Find probability of random variable.

x can go from 0 (5 times we extract two by two balls and they are with different colour) to 5 (5 times we extract two by two balls and they are with same colour). I started with P(x=0) and I stucked there. How to calculate number of all possible events when extracting two by two balls at the time and number of all possible events of interest (we extract 5 pairs of balls and they are with different colours)?
Few events of interest woul be for example:
black ball white ball, black ball white ball, black ball white ball, black ball white ball,black ball white ball or
white ball black ball, white ball black ball, white ball black ball, white ball black ball, white ball black ball or
white ball black ball, black ball white ball, black ball white ball, black ball white ball, white ball black ball
etc.

Show some work. For example, how would you compute the probability that all pairs have different colours?