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 : 11
Number of faculty members : 13
Total 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]
