Answer:
a) [tex]\frac{14}{285}[/tex]
b) [tex]\frac{11}{57}[/tex]
Step-by-step explanation:
We are given that a committee of three people is selected at random from a set of eight teachers, seven parents of students, and five alumni.
We are to find:
a) the probability the committee consists of all teachers is:
Number of ways to select three that are all teachers = [tex]8C3[/tex]
Number of ways to select three randomly = [tex]20C3[/tex]
P (3 all teachers) = [tex]\frac{8C3}{20C3}[/tex] = [tex]\frac{14}{285}[/tex]
b) the probability the committee has no teachers is:
Number of ways to select three that it has no teachers = [tex]12C3[/tex]
Number of ways to select three randomly = [tex]20C3[/tex]
P (no teachers) = [tex]\frac{12C3}{20C3}[/tex] = [tex]\frac{11}{57}[/tex]
