3.6. Basic Counting Rules http://www.ck12.org
- TheMultiplicative Rule of Countingstates: if there arenpossible outcomes for eventAandmpossible
outcomes for eventB, then there are a total ofnmpossible outcomes for the series of eventsAfollowed byB. - Thefactorial, ’!’, meansn!=n(n− 1 )(n− 2 )... 1.
- The number ofpermutations(orderedarrangements) ofndifferent objects withinrpositions isPrn=(nrn!)!
- The number ofcombinations(unorderedarrangements) ofnobjects takenrat a time isCrn=r!(nn−!r)!
Review Questions
- Determine the number of simple events when you toss a coin the following number of times: (Hint: as the
numbers get higher, you will need to develop a systematic method of counting all the outcomes)
a. Twice
b. Three times
c. Five times
d. Look for a pattern in the results of a) through c) and try to figure out the number of outcomes for tossing
a coinntimes. - Flying into Los Angeles from Washington DC, you can choose one of three airlines and can choose either first
class or economy. How many travel options do you have? - How many different 5−card hands can be chosen from a 52−card deck?
- Suppose an automobile license plate is designed to show a letter of the English alphabet, followed by a five-
digit number. How many different license plates can be issued?
Review Answers
- 4
- 8
- 32
- 2n
- 6
- 2, 598 , 960
- 2, 600 , 000