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Contents Index Dark Mode Prev Up Next \(\newcommand{\im}{{\mathrm{im}}}
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Exercises 4.3.3 Exercises
1.
Give the definition for these terms. Be sure to set up any notation that is required.
2. A local pizza shop offers their pies in small, medium, large, or extra large. For toppings, they offer: pepperoni, sausage, bacon, olives, onions, peppers, and anchovies. How many different pizzas can they make that have exactly three (different) toppings?
3.
Fifteen people on a softball team show up for a game.
How many ways are there to select 9 to take the field?
How many ways are there to assign the 9 positions?
4. How many permutations of the letters ABCDEFGH contain the string ABC?
5. In how many different orders can ten runners finish a race if no ties are allowed?
6. List all the permutations of
\(\{1,2,3\}\)
7. List all the
\(3\) -combinations of
\(\{a, e, i, o, u\}\text{.}\)
8. List all the
\(3\) -permutations of
\(\{1, 2, 3, 4, 5, 6\}\text{.}\)
9. In how many ways can a set of four letters be selected from the English alphabet?
10. How many ways are there for 10 sophomores and 6 freshmen to stand in a line if so that no two freshmen stand next to each other? (Hint: First position the sophomores and then consider the possible positions for the freshmen.)
11.
Harry, Hermione, Ron, Fred, George, Ginny, Luna, Neville, Seamus, and Hagrid go to some pictures taken.
How many ways are there to arrange four people from that group in a row for the picture?
Suppose Harry is willing to pay for any picture that he is in. How many ways are there to arrange four people from that group in a row for the picture, if Harry must be one of the four?
