3 students are selected from a class that has 10 boys and 5 girls. What is the probability that 1 boy and 2 girls are selected?

The  class  has  15  students of which 10 are boys and 5
are girls.   Three  students  are  selected  (at 
random).

We further assume that  the
selection is  made by
SRSWOR.

Total number of ways
in which 3 students can be selected from 15 students is 15 C 3 =  (15*14*13)/ 3!  =
455.

Again, 1 boy can be
selected from 10 boys in 10C1  =  10  ways.  Also,  2 girls can be selected from 5 girls
in 5C2  =  10  ways.  By multiplication principle,  the combined event  can occur in
10*10 = 100  ways.

By  using
classical definition of probability,  the required probability  is 100 / 455 = 
20 /
91.