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Glencoe Algebra 2

PT: Permutations

RW: Locker Combinations

Suppose you have forgotten you locker combination.  There are 36 numbers on the lock, and the correct combination order is right __ - left __ - right __.  How many combinations may be necessary to try in order to open the lock? (Hint: Numbers such as 3-3-3 may be repeated)

Glencoe Algebra 1, p. 413

PT: Permutations, Sample Space

RW: Archaeology

A group of college archaeology students are traveling to the Virgin Islands to study Carib Indian relics and the remnants of the forts built by the Danes.  The Carib Indians were the original occupants of the islands but had died or left by early 1600s. The Danes formally claimed the islands in 1666 and controlled them until 1917.  The group’s advisor must decide how the group will get to the Islands.  From their college, they will travel first to Miami, Florida, by car, bus, or plane.  From Miami they can reach St. Thomas in the Virgin Islands by plane or ship.  Suppose the advisor picks the mode of transportation at random.  List all possible modes of transportation to the islands.  Find the probability that they will travel by car first and then fly.

Gordon-Holliday Pre-calculus, p. 772

M: Compound and Simple Events

PT: Permutations

RW: Lotto 

The state of Pennsylvania has a Wild Card Lotto drawing twice a week in which 6 numbers out of 48 are drawn at random.  The proceeds from the lottery help finance educational programs in the state.

a)   What is the probability of winning one of the weekly Lotto drawings if you buy one ticket? 

b)   How many ways can 6 numbers be drawn?

Gordon-Holliday Pre-calculus, p. 763

M: Availability/Simple and Compound Events

PT: Permutations

RW: Morse code, Communication

Morse code is a system of dots and dashes, and spaces that telegraphers in the United States and Canada once used to send messages by wire.  How many different arrangements are there of 7 dots, 3 dashes, and 2 spaces?

Gordon-Holliday Pre-calculus, p. 763

M: Simple and Compound Events

PT: Permutations

RW: CD Changer, Music

A disc CD changer holds 5 CDs on a circular platter.  How many different ways can 5 CDs be arranged on the changer?  If all 5 CDs have 12 songs each and you put the CD changer on random (which plays all the songs on each CD once) how many different ways can all the songs be played?

Gordon-Holliday Pre-calculus, p. 756

M: Simple and Compound Events

PT: Permutations

RW: Sports/Swimming

The eight finalists in the men’s 100-meter breaststroke at the 1992 Summer Olympics were Nick Gillingham of Great Britain, Vassili Iranov of the Unified Team, Phillip of the United States, Norbert Rozsa of Hungary, Akira Hayashi of Japan, Dmitri Moorehouse of Great Britain. Medals were given to the first three swimmers to finish the race.

a)   How many ways could the medals be awarded in such a race?

b)   If all 8 swimmers finished the race, how many different orders of finish were possible?

Gerver Algebra II, p. 115

PT: Permutations

Find the number of permutations possible in this situation;

a)   7 people are seated in 7 chairs that are arranged in a line;

b)   7 people are seated in 7 chairs that are arranged in a circle;

c)   With no repetitions allowed, 2-digit numbers are formed from the digits 1, 3, 5, 7, 9;

d)   With repetitions allowed, 2-digit numbers are formed from the digits 1, 3, 5, 7, 9;

e)   8-letter arrangements are formed using the letters ELLIPSES.

Key to Problem Bank: