Download Each event can occur in the given number of ways

Honors Algebra 2
0.4 Day 2 Worksheet
Name: _____________________________________
Each event can occur in the given number of ways. Find the number of ways all of the events can occur.
1. Event 1: 6 ways, Event 2: 5 ways, Event 3: 12 ways
2. Event 1: 2 ways, Event 2: 4 ways, Event 3: 5 ways, Event 4: 3 ways
For the given configuration, determine how many different 5-digit postal zip codes are possible if (a) digits can be repeated, and (b)
digits cannot be repeated.
3. Begins with 4.
4. Has all even digits.
Find the number of distinguishable permutations of the letters in the word.
5. PAPER
6. EEL
7. MATHEMATICS
8. BILLIONAIRES
9. You have forgotten the combination of the lock on your school locker. There are 40 numbers on the lock, and the correct
combination is “R_____-L_____-R_____.” How many possible combinations are there?
In numbers 10 – 12, find the number of possible 5-card hands that contain the specified cards.
10. 4 aces and 1 king
11. 3 of one kind and 2 of a different kind
12. 3 face cards of the same suit and 2 other cards (none of which are face cards)
13. Flags of 6 countries are to be displayed in a row along the back of the stage. The flags of the two countries, A and B, must be next
to each other.
a. In how many ways can this be done if the flag of country A must be to the left of the flag of country B?
b. In how many ways can the flags be hung if the 2 flags can be in either order?
Decide whether the problem requires combinations or permutations to find the answer. Then solve the problem.
14. A pizza shop runs a special where you can buy a large pizza with one cheese, one vegetable, and meat for $9.00. You have a
choice of 7 cheeses, 11 vegetables, and 6 meats. Additionally, you have a choice of 3 crusts and 2 sauces. How many different
variations of the pizza special are possible?
15. A particular classroom has 24 seats and 19 students. Assuming the seats are not moved, how many different seating arrangements
are possible?
16. Eight members of a school marching band are auditioning for 3 drum major positions. In how many ways can students be chosen
to be drum majors?
17. Your school yearbook has an editor-in-chief and an assistant editor-in-chief. The staff of the yearbook has 15 students. In how
many ways can students be chosen for these 2 positions?
18. A discussion panel consisting of 4 women and 3 men is to be seated behind a long table at an open town meeting. In how many
ways can the panel be seated if men and women must be placed in alternate seats?
19. Each grouping in the Morse Code is a sequence of 4 or fewer dots and/or dashes that stands for a letter of the alphabet or a
punctuation mark. For example, the grouping consisting of 3 dots stands for the letter “S.” How many distinct grouping are possible
in this system?
20. An ice cream shop has a choice of 10 toppings. Suppose you can afford at most four toppings. How many different types of ice
cream sundaes can you order?
21. A college football team plays 10 games during the season. In how many ways can it end the season with 5 wins, 4 losses, and 1
tie?
22. If the NCAA has applications from 6 universities for hosting its intercollegiate tennis championships in 2008 and 2009, how many
ways may they select the hosts for these championships
a. if they are not both to be held at the same university.
b. if they may both be held at the same university.