Questions
1. Steve interviewed several musicians to be a part of his band. If he interviewed 5
guitarists, 3 drummers, and 6 vocalists, and the band consists of one guitarist, one
drummer, and one vocalist, how many different bands can Steve create?
2. License plates in Florida have the form A12BCD; that is, a letter followed by two digits
followed by three more letters.
(a) How many different license plates are possible?
(b) Griff would like a plate that ends in MWS. How many such plates are there?
3. (a) An ice cream shop has vanilla, chocolate and strawberry flavors. You also have
the choice of a sugar cone or waffle cone. Draw a tree diagram to show the different
kinds of double dip cones you could order. (Double dip means two scoops.) Assume
that choosing chocolate and then vanilla is different than choosing vanilla and then
chocolate. (So, order matters.)
(b) If you must choose two different ice cream flavors for your double dip cone, how
many possible different cones could you order?
4. A security keypad uses five digits (0 to 9) in a specific order. How many different
keypad patterns are possible if the first three digits must be even and the last digit
cannot be zero?
6. The math club needs to select a President, Vice President, Treasurer and Secretary
from their 20 members. How many ways can they do this?
7. The math club wants to choose a committee to plan the back to school party. How
many 5 person committees can be formed from the set of 20 members?
8. Two freshmen and three sophomores from a sorority will attend a conference. If the
sorority has 12 freshmen and 15 sophomores, in how many different ways can the
conference attendees be selected?
9. Faculty at a certain university need to create a committee to evaluate the general
studies curriculum offered on campus. If there are 25 faculty members and they must
select a chair, vice chair, secretary and 4 additional faculty members to be on the
committee, in how many ways can the committee be formed?
10. Sam bought 9 tickets all in the same row to a KC Royals game for himself and his
friends next week. His friends are Eric, Sarah, Renee, David, Julie, Derek, Kelsey and
Kyle.
(a) How many different ways can the friends be seated in the row?
(b) Sam has a crush on Sarah, so he wants to make sure his seat is next to hers. How
many ways are there to assign the seats now?
(c) How many ways are there to assign the seats if Sam wants to ensure that they
are all seated boy-girl-boy-girl?
