Kenneth Rosen Edition 7 Exercise 6.1 Question 1 (Page No. 396)

Question

There are $18$ mathematics majors and $325$ computer science majors at a college.

• A. In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major?
• B. In how many ways can one representative be picked who is either a mathematics major or a computer science major?

Answer 1

Before going to the answer lets recall some definitions to solve this problems.

Product Rule: If one event occur in m ways and a second event occur in n ways, the number of ways the two events occur in sequence is mxn ways.

Sum Rule: If an event occur either in m ways or in n ways (non-overlapping) , the number of ways the event can occur is m+n ways.

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Given Mathematics majors =18 and Computer science majors = 325

A. We need to use product rule, because the first event is picking up a Mathematics major and second event is picking up                computer science major.

                           = 18 x 325

                           = 5850

B. Here sum rule is applicable, because the event is picking up a mathematics major or a computer science major

                          = 18 + 325 

                          = 343 

     

Answer 2

A. The job of chossing two representative one from Mathematics major and other from Computer Science major has TWO segments.

First Segment Of Choosing A Mathematics Major Canbe Done By 8 Ways And The Second Segment Of Chossing A Computer Science Major Can Be Done In 325 Ways . Hence The Complete Job Can Be Done In 18*325 Ways=5850 Ways

 

B.Here is the job of choosing one representative has only one segment. we can choose Mathematics Major in 18 ways  and Computer science major in 325 ways. Hence choosing any representative fro Mathematics major or Computer science major can be done in 18 + 325 =343 ways.