Counting (Chapter 6) Review

Select problems from the text (© McGraw Hill)

Problem 1 ¶

How many strings of all the first seven letters of the alphabet (A, B, C, D, E, F, G) are there that contain no repeated letters and begin or end with a vowel (A or E)?

Problem 2 ¶

When you buy a Powerball ticket, you select 5 different white numbers from among the numbers 1 through 59 (order of selection does not matter), and one red number from among the numbers 1 through 35. How many different Powerball tickets can you buy?

Problem 3 ¶

How many students, each of whom comes from one of the $50$ states, must be enrolled in a university to guaranteed that there are at least 100 who come from the same state?

Problem 4 ¶

What is the coefficient of $x^9$ in $(2 − x)^{19}$?

Problem 5 ¶

A book publisher has 3000 copies of a textbook. How many ways are there to store these books in their three warehouses if the copies of the book are all the same?