examples

Question 1

A total of 28 percent of males living in Nevada smoke cigarettes, 6
percent smoke cigars, and 3 percent smoke both cigars and
cigarettes. What percentage of males smoke neither cigars nor
cigarettes?

Answer 1

Solution:
E = a cigarette smoker F = cigar smoker.
Then, the probability this person is either a cigarette or a cigar
smoker is

P(E ∪ F ) = P(E ) + P(F ) − P(EF) = .28 + .06 − .03 = .31
P(E ∪ F )^c = 1 − .31 =.69

Question 2

Mr. Jones has 10 books. 4 math, 3 chemistry, 2 history, 1 language. Jones wants to arrange his books so that all books dealing with the same subject are together on the shelf. How many different arrangements are possible?

Answer 2

The number of combinations of a set of n objects is given by n!

Thus there are 4! ways to arrange the math books internally, 3! for chem….

and there are 4! ways to arrange each group.

Thus there are 4!*4!*3!*2! = 6912 ways to arrange the books while each remains within its subject.