Question

A university has 90 faculty members: 60 male and 30 female. How many committees of size 18 can we form if:

(a) no restriction?

(b) among the selected 18 faculty members, one position is president and one is vice president?

(c) among the selected 18 faculty members, one position is president and tow are vice presidents?

(d) among the selected 18 faculty members, one position is president, one is a male vice president and one is a female vice president?

Answer 1

a)N(no restriction)=N(selecting 18 from 90 members)= =90!/(18!*72!) =3.78965*10¹⁸

b)

N( one position is president and one is vice president)=N(selecting one person from 90 for president position and then one person from 89 for f  vice president and then select 16 from remaing 88)

==1.1596*10²¹

c)

N( one position is president and two are vice president)=N(selecting one person from 90 for president position and then two person from 89 for two vice president and then select 15 from remaing 87)

= =9.2771*10²¹

d)

N(among the selected 18 faculty members, one position is president, one is a male vice president and one is a female vice president)=N(selecting one male vice president from 60 person and one female vice president from 30 and then one president from remaing 88 people amd then 15  from remaing 87 )

=

=4.1695*10²¹