In a class, there are 10 boys and 8 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is:

Question: In a class, there are 10 boys and 8 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is:

Solution:
Total students = 10 + 8 = 18
Let S be the sample space, and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number of ways of selecting 3 students out of 18 = ¹⁸C₃
= (18 × 17 × 16)/(3 × 2 × 1)
= 816

And, n(E) = Number of events of selecting 1 girl and 2 boys = ⁸C₁ × ¹⁰C₂
= 8 × [(10 × 9)/2]
= 8 × 45
= 360

∴ Probability = n(E)/n(S)
= 360/816
= 15/34