Question

A bag contains 7 orange balls and 3 blue balls, 4 balls are selected at random from the bag,
without replacement. Let X denote the number of blue balls selected. How do I work out P(X=2) and P (X=3) and p(X=4) ???

Answer 1

If your problem is determining P(X>=1), we can try to cal P(X=0), then
P(X>=1) = 1 - P(X = 0)
Or, as you want,
P(X=2) = C(2,3)*C(2,7) / C(4,10)
C(m,n) is number of way to collect m balls from n balls.