There are 12 boys and 8 girls in a tution centre If three of them scored first mark then what is the...........

Explanation:

Total number of students = 20.

Let S be the sample space.
Then, n(S) = number of ways of three scored first mark
n(S) = 20C3 = 20 x 19 x 18 / 2 x 3 = 20 x 19 x 3

Let, E be the event of 1 girl and 2 boys.
Therefore, n(E) = number of possible of 1 girl out of 8 and 2 boys out of 12.
n(E) = 8C1 x 12C2 = 8 x 12 x 11 / 1 x 2 = 8 x 6 x 11.

Now, the required probability = n(E)/n(S) = (8 x 6 x 11)/(20 x 19 x 3) = 44/95.

Hence, option 3 is the correct answer.