Chapter 16

A given region has the telephone prefix 472. a. How many 7-digit telephone numbers are possible with this prefix? b. How many of these possibilities end with 4 unique digits? c. How many of these possibilities form an even number?

How many 2-letter patterns can be formed from the alphabet if the first letter is a vowel (A, E, I, O, U) and the second letter is a consonant that occurs later in the alphabet than the vowel in the first position?

How many 2-letter patterns may be formed from the alphabet if the first letter is a consonant and the second letter is a vowel that occurs earlier than the first letter?

\(\ln 38-43,\) solve for \(x\) $$ _{12} C_{4}=_{x} C_{8} $$

Show that \(_{n} C_{r}=_{n} C_{n-r}\)

At the library, Jordan selects 8 books that he would like to read but decides to check out just 5 of them. How many different selections can he make?

Eli has homework assignments for 5 subjects but decides to complete 4 of them today and complete the fifth before class tomorrow. In how many different orders can he choose 4 of the 5 assignments to complete today?

There are 12 boys and 13 girls assigned to a class. In how many ways can 2 boys and 3 girls be selected to transfer to a different class?

In how many ways can the letters of CIRCLE be arranged if the first and last must be consonants?

In how many ways can 6 transfer students be assigned to seats in a classroom that has 10 empty seats?

From a standard deck of 52 cards, how many hands of 5 cards can be dealt?

A local convenience store hires three students to work after school. Next month, there are 20 days on which they will work. Alex will work 8 days, Rosa will work 6 days, and Carla will work 6 days. In how many ways can their schedule for the month be arranged?

Marie has an English assignment and a history assignment that require research in the library. She makes a schedule for the 5 days of this week to work on the English assignment for 2 days and the history assignment for 3 days. How many different schedules are possible?

Roy and Valerie are playing a game of tic-tac-toe. In how many different ways can the first 4 moves in the game be made?

Rafael is running for mayor of his town. He sent out a survey asking his constituents to rank the following issues in order of importance to them: crime, unemployment, air quality, schools, public transportation, parking, and taxes. a. How many different rankings are possible? b. What fraction of the possible rankings put crime first? c. How many of the possible rankings are in alphabetical order?

The Electronic Depot received 108 \(\mathrm{mp} 3\) players, 12 of which are defective. In how many different ways can 6 players be selected for display such that: a. none are defective? b. half are defective? c. all are defective?

The program director at the local sports center wants to schedule the following classes on Wednesdays: aerobics, tai chi, yoga, modern dance, fitness, and weight training. Starting at \(9 : 00\) A.M. each class begins on the hour and ends at 10 minutes before the hour. a. How many different ways can the classes be scheduled? b. If the yoga instructor is available only for a \(9 : 00\) A.M.class, how many different ways can the classes be scheduled?

A medical researcher has received approval to test a new combination drug therapy. A total of 6 doses of drug \(\mathrm{X}, 3\) doses of drug \(\mathrm{Y},\) and 4 doses of drug \(\mathrm{Z}\) are to be given on successive days. The researcher wants to determine if some orders are more effective than others. How many different orders are possible?