Question 1

How many permutations of all 26 letters of the alphabet are there that contain none of the words: SAVE, PLAY, SNOW?

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Question 2

A market sells ten kinds of soda. You want to buy 12 bottles. How many possibilities are there? if you want at most three bottles of any kind?

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Question 3

A market sells ten kinds of soda. You want to buy 12 bottles. How many possibilities are there if you want (a) at least one of each kind? (b) at most seven bottles of any kind?

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Question 4

Suppose you have 100 identical marbles and ﬁve jars (labeled A, B, C, D, E). In how many ways can you put the marbles in the jars if: (a) each jar has at least six marbles in it? (b) each jar has at most forty marbles in it?

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Question 5

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words SWORD, PLANT, CARTS?

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Question 6

An oﬃce manager has four employees and nine reports to be done. In how many ways can the reports be assigned to the employees so that each employee has at least one report to do.

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Question 7

Suppose $|A|$ =8  and $| B |$  =4 .  Find the number of functions $f : A \rightarrow B$ that are onto $B$.

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Question 8

How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

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Question 9

A doughnut shop sells 20 kinds of doughnuts. You want to buy 30 doughnuts. How many possibilities are there if you want at most six of any one kind?

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Question 10

Find the number of positive integers $\leq 1000 \text { that are multiples of at least one of } 3,4,12 \text {. }$

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Question 11

A market sells 40 kinds of candy bars. You want to buy 15 candy bars. (a) How many possibilities are there? (b) How many possibilities are there if you want at least three peanut butter bars and at least ﬁve almond bars? (c) How many possibilities are there if you want exactly three peanut butter bars and exactly ﬁve almond bars? (d) How many possibilities are there if you want at most four toﬀee bars and at most six mint bars?

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Question 12

How many permutations of the 26 letters of the alphabet are there that do not contain any of the following strings: LOP, SLOP, SLOPE, LOPE.

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Question 13

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words: CAR, CARE, SCAR, SCARE?

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Question 14

How many ways are there to choose ﬁve donuts if there are eight varieties and only the type of each donut

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Question 15

A doughnut shop sells 20 kinds of doughnuts. You want to buy 30 doughnuts. How many possibilities are there if you want at most 12 of any one kind?

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Question 16

Find the number of positive integers $< 1000 \text { that are multiples of at least one of } 2,6,12 \text {. }$

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Question 17

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words DOG, BIG, OIL?

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Question 18

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words CART, SHOW, LIKE?

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Question 19

Suppose $| A | = | B | = | C | = 100 , | A \cap B | = 60 , | A \cap C | = 50 , | B \cap C | = 40 \text {, and } | A \cup B \cup C | = 175$ . How many elements are in $A \cap B \cap C$?

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Question 20

You have ten cards, numbered 1 through 10. In how many ways can you put the ten cards in a row so that card i is not in spot i, for i = 1, 2, . . . , 10?

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Quiz 8: A: Advanced Counting Techniques

How many permutations of all 26 letters of the alphabet are there that contain none of the words: SAVE, PLAY, SNOW?

A market sells ten kinds of soda. You want to buy 12 bottles. How many possibilities are there? if you want at most three bottles of any kind?

A market sells ten kinds of soda. You want to buy 12 bottles. How many possibilities are there if you want (a) at least one of each kind? (b) at most seven bottles of any kind?

Suppose you have 100 identical marbles and ﬁve jars (labeled A, B, C, D, E). In how many ways can you put the marbles in the jars if: (a) each jar has at least six marbles in it? (b) each jar has at most forty marbles in it?

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words SWORD, PLANT, CARTS?

An oﬃce manager has four employees and nine reports to be done. In how many ways can the reports be assigned to the employees so that each employee has at least one report to do.

Suppose $|A|$ =8 and $| B |$ =4 . Find the number of functions $f : A \rightarrow B$ that are onto $B$ .

How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

A doughnut shop sells 20 kinds of doughnuts. You want to buy 30 doughnuts. How many possibilities are there if you want at most six of any one kind?

Find the number of positive integers $\leq 1000 \text { that are multiples of at least one of } 3,4,12 \text {. }$

How many permutations of the 26 letters of the alphabet are there that do not contain any of the following strings: LOP, SLOP, SLOPE, LOPE.

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words: CAR, CARE, SCAR, SCARE?

How many ways are there to choose ﬁve donuts if there are eight varieties and only the type of each donut

A doughnut shop sells 20 kinds of doughnuts. You want to buy 30 doughnuts. How many possibilities are there if you want at most 12 of any one kind?

Find the number of positive integers $< 1000 \text { that are multiples of at least one of } 2,6,12 \text {. }$

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words DOG, BIG, OIL?

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words CART, SHOW, LIKE?

Suppose $| A | = | B | = | C | = 100 , | A \cap B | = 60 , | A \cap C | = 50 , | B \cap C | = 40 \text {, and } | A \cup B \cup C | = 175$ . How many elements are in $A \cap B \cap C$ ?

You have ten cards, numbered 1 through 10. In how many ways can you put the ten cards in a row so that card i is not in spot i, for i = 1, 2, . . . , 10?

Quiz 8: A: Advanced Counting Techniques

How many permutations of all 26 letters of the alphabet are there that contain none of the words: SAVE, PLAY, SNOW?

A market sells ten kinds of soda. You want to buy 12 bottles. How many possibilities are there? if you want at most three bottles of any kind?

A market sells ten kinds of soda. You want to buy 12 bottles. How many possibilities are there if you want (a) at least one of each kind? (b) at most seven bottles of any kind?

Suppose you have 100 identical marbles and ﬁve jars (labeled A, B, C, D, E). In how many ways can you put the marbles in the jars if: (a) each jar has at least six marbles in it? (b) each jar has at most forty marbles in it?

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words SWORD, PLANT, CARTS?

An oﬃce manager has four employees and nine reports to be done. In how many ways can the reports be assigned to the employees so that each employee has at least one report to do.

Suppose ∣A∣|A|∣A∣ =8 and ∣B∣| B |∣B∣ =4 . Find the number of functions f:A→Bf : A \rightarrow Bf:A→B that are onto BBB .

How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

A doughnut shop sells 20 kinds of doughnuts. You want to buy 30 doughnuts. How many possibilities are there if you want at most six of any one kind?

Find the number of positive integers ≤1000 that are multiples of at least one of 3,4,12. \leq 1000 \text { that are multiples of at least one of } 3,4,12 \text {. }≤1000 that are multiples of at least one of 3,4,12.

How many permutations of the 26 letters of the alphabet are there that do not contain any of the following strings: LOP, SLOP, SLOPE, LOPE.

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words: CAR, CARE, SCAR, SCARE?

How many ways are there to choose ﬁve donuts if there are eight varieties and only the type of each donut

A doughnut shop sells 20 kinds of doughnuts. You want to buy 30 doughnuts. How many possibilities are there if you want at most 12 of any one kind?

Find the number of positive integers <1000 that are multiples of at least one of 2,6,12. < 1000 \text { that are multiples of at least one of } 2,6,12 \text {. }<1000 that are multiples of at least one of 2,6,12.

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words DOG, BIG, OIL?

How many permutations of all 26 letters of the alphabet are there that contain at least one of the words CART, SHOW, LIKE?

You have ten cards, numbered 1 through 10. In how many ways can you put the ten cards in a row so that card i is not in spot i, for i = 1, 2, . . . , 10?

Suppose $|A|$ =8 and $| B |$ =4 . Find the number of functions $f : A \rightarrow B$ that are onto $B$ .

Find the number of positive integers $\leq 1000 \text { that are multiples of at least one of } 3,4,12 \text {. }$

Find the number of positive integers $< 1000 \text { that are multiples of at least one of } 2,6,12 \text {. }$