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Answered

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A history class is comprised of 10 female and 8 male students. If the instructor of the class randomly chooses 14 students from the class for an oral exam, what is the probability that 8 female students and 6 male students will be selected? Round your answer to 3 decimal places.

Sagot :

reinhard10158

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

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