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?
Accepted Solution
A:
Answer: a) [tex]\dfrac{3}{874}[/tex]b) [tex]\dfrac{30}{3059}[/tex]c) [tex]\dfrac{3575}{12236}[/tex]Step-by-step explanation:Given : Number of students : 11Number of faculty members : 13Total persons : [tex]11+13=24[/tex]Total number of ways to structure a jury of six people from a group of 24 people :-[tex]^{24}C_{6}=\dfrac{24!}{6!(24-6)!}=134596[/tex]a) Number of ways of selecting a jury of all students :-[tex]^{11}C_{6}=\dfrac{11!}{6!(11-6)!}=462[/tex]Then , the probability of selecting a jury of all students :-[tex]\dfrac{462}{134596}=\dfrac{3}{874}[/tex]b) Number of ways of selecting a jury of all faculty :-[tex]^{13}C_{6}=\dfrac{13!}{6!(13-6)!}=462[/tex]Then , the probability of selecting a jury of all students :-[tex]\dfrac{1716}{134596}=\dfrac{30}{3059}[/tex]c) Number of ways of selecting a jury of two students and four faculty :-[tex]^{11}C_{2}\times^{13}C_{4}=\dfrac{11!}{2!(11-2)!}\times\dfrac{13!}{4!(13-4)!}=39325[/tex]Then , the probability of selecting a jury of all students :-[tex]\dfrac{39325}{134596}=\dfrac{3575}{12236}[/tex]