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=[tex]^{20}C_8=\frac{20!}{(20-8)!\times8!}=125970[/tex]
The number of ways of selecting jury of all faculty=[tex]^9C_8=\frac{9!}{8!(9-8)!}=9[/tex]
The probability of selecting a jury of all faculty=[tex]\frac{9}{125970}=0.000071[/tex]
The number of ways of selecting jury of six students and two two faculty
[tex]=^9C_6\times ^{11}C_2=\frac{9!}{6!(9-6)!}\times\frac{11!}{2!\times(11-2)!}\\=84\times55=4620[/tex]
Now, the probability of selecting a jury of six students and two two faculty
[tex]=\frac{4620}{125970}=0.03667[/tex]
