Find the probability of selecting four purple balls at random out of ten balls, six are purple?

What is the probability of selecting four purple ball at random out of ten balls, six of which are purple?
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There is a 6/10 probability of drawing the first purple ball; the probability of the second ball being purple is 5/9 because there's one ball fewer and only 5 of them are purple; the probability of the third ball being purple is 4/8; and the 4th ball, 3/7. The combined probability is 6*5*4*3/(10*9*8*7)=1/14 or about 7.14%.

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