Question 675607
The C's are part of a symbol that means combinations.
Unfortunately different names and symbols are used in different textbooks.
To make matters worse, the symbol is hard to render, meaning that what you would write with pencil and paper may be impossible to type.
"10C2" meant the number of combinations of 10 taken 2 at a time,
meaning the number of sets of 2 girls that could be made from the 10 girls in the class.
That was {{{10*9/2=45}}}
"(10+x)C2" meant the number of combinations of 10+x taken 2 at a time,
meaning the number of sets of students that could be made from the 10 girls plus x boys in the class.
That was calculated as {{{(10+x)(9+x)/2}}}.
Then, the ratio of all the number of possible sets of 2 girls,
divided by number of all possible sets of 2 pupils,
was set as equal to the probability of having 2 girls as the set of 2 pupils selected at random: 0.15.
{{{0.15}}}={{{45/((10+x)(9+x)/2)}}} --> {{{0.15= 45*(2/((10+x)(9+x)))}}} --> {{{0.15= 90/((10+x)(9+x))}}} --> {{{15/100= 90/((10+x)(9+x))}}}
Then, dividing both sides of the equal sign by {{{15}}},
{{{15/100= 90/((10+x)(9+x))}}} --> {{{1/100= 6/((10+x)(9+x))}}}
And cross-multiplying, or going through a couple of dividing/multiplying  both sides of the equal sign by the same number,
{{{1/100= 6/((10+x)(9+x))}}} --> {{{600=(10+x)(9+x)}}}