Question

The grade appeal process at a university requires that a jury be structured by selecting six individuals randomly from a pool of eleven students and thirteen 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 two students and four ​faculty?

Answer 1

Answer: a) $\dfrac{3}{874}$

b) $\dfrac{30}{3059}$

c) $\dfrac{3575}{12236}$

Step-by-step explanation:

Given : Number of students : 11

Number of faculty members : 13

Total persons : $11+13=24$

Total number of ways to structure a jury of six people from a group of 24 people :-

$^{24}C_{6}=\dfrac{24!}{6!(24-6)!}=134596$

a) Number of ways of selecting a jury of all​ students :-

$^{11}C_{6}=\dfrac{11!}{6!(11-6)!}=462$

Then , the probability of selecting a jury of all​ students :-

$\dfrac{462}{134596}=\dfrac{3}{874}$

b) Number of ways of selecting a jury of all​ faculty :-

$^{13}C_{6}=\dfrac{13!}{6!(13-6)!}=462$

Then , the probability of selecting a jury of all​ students :-

$\dfrac{1716}{134596}=\dfrac{30}{3059}$

c) Number of ways of selecting a jury of two students and four ​faculty :-

$^{11}C_{2}\times^{13}C_{4}=\dfrac{11!}{2!(11-2)!}\times\dfrac{13!}{4!(13-4)!}=39325$

Then , the probability of selecting a jury of all​ students :-

$\dfrac{39325}{134596}=\dfrac{3575}{12236}$