There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?

• Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
  
  Then, n(S) = Number ways of selecting 3 students out of 25
  = 25C3 `
  = (25 x 24 x 23)
  (3 x 2 x 1)
  = 2300.
  n(E) = (10C1 x 15C2)
  = 10 x (15 x 14)
  (2 x 1)
  = 1050.
  P(E) = n(E) = 1050 = 21 .
  n(S) 2300 46
  
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