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The grade appeal process at a university requires that a jury be structured by selecting seven individuals randomly from a pool of ten students and eleven faculty.​ (a) What is the probability of selecting a jury of all​ students? (b) What is the probability of selecting a jury of all​ faculty? (c) What is the probability of selecting a jury of four students and three ​faculty?
​(a) What is the probability of selecting a jury of all​ students?
nothing ​(Round to five decimal places as​ needed.)
​(b) What is the probability of selecting a jury of all​ faculty?
nothing ​(Round to five decimal places as​ needed.)
​(c) What is the probability of selecting a jury of four students and three ​faculty?
nothing ​(Round to five decimal places as​ needed.)

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Step-by-step explanation:

There are 10 students and 11 faculty, for a total of 21 people.

7 individuals are chosen for the jury.

(a) There are ₁₀C₇ ways of choosing 7 individuals from 10 students.

There are ₂₁C₇ ways of choosing 7 individuals from 21 people.

So the probability that the individuals are all students is:

P = ₁₀C₇ / ₂₁C₇

P = 120 / 116280

P ≈ 0.00103

(b) There are ₁₁C₇ ways of choosing 7 individuals from 11 faculty.

There are ₂₁C₇ ways of choosing 7 individuals from 21 people.

So the probability that the individuals are all students is:

P = ₁₁C₇ / ₂₁C₇

P = 330 / 116280

P ≈ 0.00284

(c) There are ₁₀C₄ ways of choosing 4 individuals from 10 students.

There are ₁₁C₃ ways of choosing 3 individuals from 11 faculty.

There are ₂₁C₇ ways of choosing 7 individuals from 21 people.

So the probability that the individuals are all students is:

P = ₁₀C₄ ₁₁C₃ / ₂₁C₇

P = 210 × 165 / 116280

P ≈ 0.29799

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