Question

1. There are 18 mathematics majors and 325 computer sci- ence majors at a college. a) Inhowmanywayscantworepresentativesbepicked 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 sci- ence major?

Answer 1

a) 5850 ways

b) 343 ways

Explanation:

Let Me represent mathematics major

Let C represent computer science major

n(M) = 18

n(C) = 325

a) The number of ways of picking a mathematics major = 18C1

Recall that nCr = n! / (n-r)! r!

18C1 = 18!/(18-1)! 1!

= 18! / 17! 1!

= 18ways

The number of ways of picking a computer science major = 325C1

= 325! / (325 -1)! 1!

= 325! / 324! 1!

= 325 ways

To know the number of ways two representatives can be picked so that one is a mathematics major and the other is a computer science major, we will use the product rule. We have

18 * 325

= 5850 ways

b) To know the number of ways two representatives can be picked so that with one is a mathematics major or the other is a computer science major, we will use the sum rule. We have 18 + 325

= 343 ways