Chapter 1 Supplementary 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?
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? 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?
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? (b) How many ways are there to pair off eight women at the dance with eight of these 12 men?
Problem 8
In how many ways can the letters in WONDERING be arranged with exactly two consecutive vowels?
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 from
a) the small red wooden square block in exactly one way?
(For example, the small red plastic square block is one such block.) b) the large blue plastic hexagonal block in exactly two ways? (For example, the small red plastic hexagonal block is one such block.)
Problem 15(a)
a) How many of the 9000 four-digit integers 1000, 1001,
1002, . . . , 9998, 9999 have four distinct digits that are either increasing (as in 1347 and 6789) or decreasing (as in
6421 and 8653)?
b) How many of the 9000 four-digit integers 1000, 1001,
1002, . . . , 9998, 9999 have four digits that are either nondecreasing