5. A certain manager has 18 employees that she must supervise. Twelve of these employees are college students and six are not college students.

Part a.

Total number of employees = 18

Out of 18 we need to select 4 peoples

For 1st selection total possible outcome = 18

From 18 employees we select 1st person, to select second person total possible outcomes 17.

From 17 employees we select 2nd person, to select 3rd person total possible outcomes 16.

From 16 employees we select 3rd person, to select 4th person total possible outcomes 15.

From 15 employees we select 4th person.

Total possible outcomes : 18x17x16x15 = 73440

Or we can use

n = total employees = 18

x = number of person selected =4

using permuation formula :

18 P4 = 18!/(18-4)! = 18! / 14! = (18x17x16x15x14!) /14! = 18x17x16x15=73440

Answer : 73440 total groups are possible.

Part. b

Total Number of college students = 12

Total Number of not college students = 6

Here we are selecting 2 college and 2 not college

Selecting Two college students

12P2 = 12!(12-2)! = 12!/10! = (12x11x10! )/10! = 12x11 =132

Selecting Two not college students

6P2 = 6!/(6-2)! = 6!/4! = (6x5x4!)/4! = 6x5 = 30

Number of way selecting 2 college and 2 non-college students =132x30 = 3960

Answer : 3960