Step-by-step explanation:
I assume that one a student is picked for an oral exam, the same student will not be picked again.
the total number of possibilities to pick 14 students out of 18 is C(18, 14) = 18!/(14! × (18-14)!) = 18!/(14! × 4!) =
= 18×17×16×15/(4×3×2) = 18×17×2×5 =
= 3,060
how many of these possibilities contain exactly 8 girls and 6 boys ?
so, we choose 8 out of the 10 girls, and 6 out of the 8 boys.
that means
C(10, 8) × C(8, 6) = 10!/(8! × 2) × 8!/(6! × 2) =
= 10×9/2 × 8×7/2 = 5×9 × 4×7 =
= 45 × 28 = 1,260
so, the probability to have 8 girls and 6 boys in a random selection of 14 students out of 18 is
1260/3060 = 21/51 = 7/17 = 0.411764706... ≈ 0.412
