Chapter 1Supplementary Exercises
Problem 1
In the manufacture of a certain type of automobile, four
kinds of major defects and seven kinds of minor defects can
occur. For those situations in which defects do occur, in how
many ways can there be twice as many minor defects as there
are major ones?Number of defects will be n
So number of minor defects will be 2n
2n ≠0 – note: this is because the defects might or might not occur
seriesSum(4n X 7(2n,3)
=4x 21 + 6x 35 + 4x 7
=84 + 210 +28
=322 ways
Problem 2
A machine has nine different dials, each with five settings
labeled 0, 1, 2, 3, and 4.
a) In how many ways can all the dials on the machine be
set?If you have 9 dials each have 5 different settings you will get
5^9 or 1953125
b) If the nine dials are arranged in a line at the top of the
machine, how many of the machine settings have no two
adjacent dials with the same setting?
=
= 5 X 65536
= 327680
Problem 7
There are 12 men at a dance. (a) In how many ways can
eight of them be selected to form a cleanup crew?8 men to be selected out of 12. The number of possible combinations would be (12, 8) = 495
(b) Howmany ways are there to pair off eight women at the dance with
eight of these 12 men?When you pair each woman with man you will start with 1st woman can be paired with 12 men, 2nd woman with 11 men and so on. When you get to the 8th woman you can be paired with 5 men. The solution goes (12*11*10*9*8*7*6*5 = 1995480)
Problem 8
In how many ways can the letters in WONDERING be
arranged with exactly two consecutive vowels?
Vowels are O-E-I
(3) x 2 x [ 2x6 + 6x5] =
6 x 42 x 720= 181440
Problem 9
Dustin has a set of 180 distinct blocks. Each of these blocks
is made of either wood or plastic and comes in one of three sizes
(small, medium, large), five colors (red, white, blue, yellow,
green), and six shapes (triangular, square, rectangular, hexagonal,
octagonal, circular). How many of the blocks in this set
differ...