The Bronx High School of Science
Mathematics Department
Jean M. Donahue, Principal
Rosemarie Jahoda, A.P. of Mathematics
Ms. Perez (
perez4@bxscience.edu
)
May 24, 2016
Fundamental Counting Principles
1.
Pat’s Pizza Palace will prepare pizza with a thick crust, with a thick crust, or in deep dish style. There are eight
choices of toppings. In how many ways can you choose a one-‐topping pizza?
ANS: 24
2.
How many odd numbers between 10 and 1000 start and end with the same digit?
ANS: 55
1*5 + 1*10*5
3.
How many license plates of 2 symbols (letters and digits) can be made using at least one letter in each?
ANS: 1196
26*10*2(order) + 26*26
OR
36*36 – 10*10
4.
Elena can wear one of 2 blouses and one of 5 scarves. How many blouse scarf combinations are available to her?
ANS: 10
5.
There are 3 trails on the north face of Mount Ezra and 2 trails on the south face of Mount Ezra. How many
routes are there going up the north face and going down the south face?
ANS: 6
6.
Kelly must buy hamburger rolls for a cookout. She can buy them in one of 4 supermarkets or one of 3 bakery
shops. In how many ways can Kelly run her errand?
ANS: 7
7.
George can choose among 15 different flavors of ice cream, 6 different flavors of sherbet, and 5 different flavors
of frozen yogurt. In how many ways can he choose a single dessert?
ANS: 26
8.
Identification labels are composed of four letters. How many different labels are possible?
ANS: 456,976
9.
Adele can take one of three buses to work or she can ride one of two trains and then walk along one of four
different routes from the train station to her office. In how many ways can Adele go to work?
ANS: 11
10.
Brenda’s school offers 5 English courses, 4 math courses, and 4 science courses. How many schedules are
possible if Brenda chooses a course in each subject?
ANS: 80
11.
One hundred cards are numbered 1 to 100. How many ways are there of choosing two cards if the first card is
not returned to the deck?
ANS: 9,900
12.
Repeat the previous exercise if the first card is returned to the deck before the second card is choses.
ANS: 10,000
13.
Suppose you have totally forgotten the combination to your locker. There are three numbers in the
combination, and you’re sure each number is different. The numbers on the lock’s dial range from 0 to 35. If you
test one combination every 12 seconds, how long will it take to test all possible combinations?
ANS: 8568 min ~ 6 days
14.
Protein molecules are made up of many amino acid residues joined end-‐to-‐end. Proteins have different
properties, depending on the sequence of amino acid residues in the molecules. If there are 20 naturally
occurring amino acids, how many different sequences of amino acid residues can occur in a 6-‐residue-‐long
fragment of a protein molecule?
ANS: 64,000,000
15.
How many multiples of 3 less than 100 can be formed from the digits 1, 4, 5, 7 and 8?
ANS: 12
