Section 4.4 Permutations and Combinations
291
65. How many committees with at least 2 delegates from Nevada are possible?
66. How many committees with at most 4 delegates total from Arizona and California are possible?
In Exercises 67–70, a hostess wishes to invite 6 dinner guests from a list of 14 friends.
67. How many sets of guests are possible?
68. How many sets of guests are possible if 6 friends are boring and 6 friends are interesting, and the hostess
wants to have at least 1 of each?
69. How many sets of guests are possible if 2 of the friends dislike each other and neither will come if the
other is present?
70. How many sets of guests are possible if 2 of the friends are very fond of each other and one won’t come
without the other?
71. Twenty-five people, including Simon and Yuan, are candidates to serve on a committee of 5. How many
committees that include Simon or Yuan are possible?
72. A student must select 5 classes for the next semester from among 12, but one of the classes must be either
American history or English literature. How many sets of classes are possible?
73. How many 5-card hands from a standard 52-card deck contain exactly 4 aces and exactly 1 club?
74. How many 5-card hands from a standard 52-card deck contain exactly 3 jacks and exactly 2 hearts?
75. How many distinct permutations of the characters in ERROR are there? (Remember that the various R’s
cannot be distinguished from one another.)
76. How many distinct permutations of the characters in LOLLAPALOOZA are there?
77. a. How many distinct permutations of the characters in the word HAWAIIAN are there?
b. How many of the permutations begin with H?
78. a. How many distinct permutations of the characters in the word APALACHICOLA are there?
b. How many of the permutations have both L’s together?
79. A bookstore displays a shelf of 5, 3, and 4 copies, respectively, of the top 3 bestsellers. How many distinguishable arrangements of these books are there if books with the same title are not distinguishable?
80. The United Group for Divisive Action uses secret code words that are permutations of 5 characters. You
learn that there are only 10 code words. What can you say about repeated characters in the code words?
81. At a dinner party for 5, a tray of 5 servings of appetizers is prepared. An appetizer could be escargots, egg
rolls, or nachos. How many different trays could the kitchen produce?
82. A florist has a large number of roses, carnations, lilies, and snapdragons in stock. How many different
bouquets of one dozen flowers can be made?
83. A cheese shop carries a large stock of 34 kinds of cheese. By the end of the day, 48 cheese sales have been
made, and the items sold must be restocked. How many different restocking orders are possible?
84. One “game package” consists of 12 bingo cards. How many different game packages are there if there are
15 kinds of cards and repetitions are allowed?
85. A hardware shipping order contains 6 items, where each item is either a gallon of paint, a hammer, or a
drill.
a. How many different shipping orders are possible?
b. How many different shipping orders are possible if no paint is shipped?
c. How many different shipping orders are possible if each order must contain at least 1 gallon of paint,
1 hammer, and 1 drill?
291
65. How many committees with at least 2 delegates from Nevada are possible?
66. How many committees with at most 4 delegates total from Arizona and California are possible?
In Exercises 67–70, a hostess wishes to invite 6 dinner guests from a list of 14 friends.
67. How many sets of guests are possible?
68. How many sets of guests are possible if 6 friends are boring and 6 friends are interesting, and the hostess
wants to have at least 1 of each?
69. How many sets of guests are possible if 2 of the friends dislike each other and neither will come if the
other is present?
70. How many sets of guests are possible if 2 of the friends are very fond of each other and one won’t come
without the other?
71. Twenty-five people, including Simon and Yuan, are candidates to serve on a committee of 5. How many
committees that include Simon or Yuan are possible?
72. A student must select 5 classes for the next semester from among 12, but one of the classes must be either
American history or English literature. How many sets of classes are possible?
73. How many 5-card hands from a standard 52-card deck contain exactly 4 aces and exactly 1 club?
74. How many 5-card hands from a standard 52-card deck contain exactly 3 jacks and exactly 2 hearts?
75. How many distinct permutations of the characters in ERROR are there? (Remember that the various R’s
cannot be distinguished from one another.)
76. How many distinct permutations of the characters in LOLLAPALOOZA are there?
77. a. How many distinct permutations of the characters in the word HAWAIIAN are there?
b. How many of the permutations begin with H?
78. a. How many distinct permutations of the characters in the word APALACHICOLA are there?
b. How many of the permutations have both L’s together?
79. A bookstore displays a shelf of 5, 3, and 4 copies, respectively, of the top 3 bestsellers. How many distinguishable arrangements of these books are there if books with the same title are not distinguishable?
80. The United Group for Divisive Action uses secret code words that are permutations of 5 characters. You
learn that there are only 10 code words. What can you say about repeated characters in the code words?
81. At a dinner party for 5, a tray of 5 servings of appetizers is prepared. An appetizer could be escargots, egg
rolls, or nachos. How many different trays could the kitchen produce?
82. A florist has a large number of roses, carnations, lilies, and snapdragons in stock. How many different
bouquets of one dozen flowers can be made?
83. A cheese shop carries a large stock of 34 kinds of cheese. By the end of the day, 48 cheese sales have been
made, and the items sold must be restocked. How many different restocking orders are possible?
84. One “game package” consists of 12 bingo cards. How many different game packages are there if there are
15 kinds of cards and repetitions are allowed?
85. A hardware shipping order contains 6 items, where each item is either a gallon of paint, a hammer, or a
drill.
a. How many different shipping orders are possible?
b. How many different shipping orders are possible if no paint is shipped?
c. How many different shipping orders are possible if each order must contain at least 1 gallon of paint,
1 hammer, and 1 drill?