Question

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

Answer 1

Answer: The probability of selecting a jury of all​ faculty=0.000071

The probability of selecting a jury of six students and two two ​faculty=0.3667

Step-by-step explanation:

Given: The number of students = 9

The number of faculty members=11

The total number of ways of selecting jury of eight individuals=$^{20}C_8=\frac{20!}{(20-8)!\times8!}=125970$

The number of ways of selecting jury of all faculty=$^9C_8=\frac{9!}{8!(9-8)!}=9$

The probability of selecting a jury of all​ faculty=$\frac{9}{125970}=0.000071$

The number of ways of selecting jury of six students and two two ​faculty

$=^9C_6\times ^{11}C_2=\frac{9!}{6!(9-6)!}\times\frac{11!}{2!\times(11-2)!}\\=84\times55=4620$

Now, the probability of selecting a jury of six students and two two ​faculty

$=\frac{4620}{125970}=0.03667$