There are 6 girls and 7 boys in a class. a team of 10 players is to be selected from the class. if the selection is random, what is the probability of selecting a team of 4 girls and 6 boys?

There are 13 students in the class.  p = probability
p  1st girl is 6/13
p 2nd girl is 5/12
p 3rd girl is 4/11
p 4th girl is 3/10
p 1rst boy is 7/9
p of 2nd boy is 6/8 
p of 3rd boy is 5/7
p of 4th boy is 4/6
p of 5th boy is 3/5
p of 6th boy is 2/4
I multiplied all of the fractions above (cancelling wherever I could and again to check my work I reduced fractions that could be and cancelled again) and I got 
1/572

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