8 professors and 11 students are available to serve on committee. (a) How many ways can a committee of four people be selected? (b) How many committees can be formed if each committee must have 3 professors and 4 students?

a) 3876   b) 18480

Step-by-step explanation:

Given , The number of professors = 8

The number of students are available = 11

Total persons = 8+11=19

a) The number of ways to select 4 people =

Hence, the number of ways to select 4 people  = 3876.

b) Number of ways to choose 3 professors and 4 students =

Hence, the numbers of ways to form a committee with 3 professors and 4 students = 18480.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2