Question

Problem 3 Consider that 200 students are set to enroll in an engineering program at some university that offers majors in four engineering disciplines: electrical, mechanical, civil, and chemical. Determine the following:

a) How many possible combinations are there for student enrollment in these four programs?

b) If every student enrollment combination is equally likely, then how probable is it that one program will have zero students enrolled in it?

c) If every student enrollment combination is equally likely, then how probable is it that one program will have every student enrolled in it?

Answer 1

Answer:

a)

Every understudy can try out any of the four projects in 4 different ways .

Number of potential ways 200 understudies take on four projects is 4^200

= 2.5822*e^120

b)

One program will have no understudies, that is three projects has all the understudies. 3 projects out of 4 is picked is 4C3 = 4 different ways .

At that point 200 understudies can take on any three projects in 3^200 different ways

We realize that

Likelihood of an occasion = great number of results/all out number of results

absolute number of results = 4^200

good number of results = 4*3^200

Likelihood that one program will have no understudies = 4*3^200 / 4^200

= 4.11446*e-25

c)

One program out of four is picked in 4 different ways.

200 understudies try out one program in 1^200 manners

In this manner ,

Likelihood that one program will have all the understudies = 4/4^200

=1.549*e^-120