3 Algebra II
Notes 12.1 Fundamental Counting Principle and Statistics
You own a pizza shop. You have thin crust pizza and deep dish pizza. You also offer several topping
choices which include pepperoni, green pepper, mushroom, sausage, and olives. How many onetopping pizza varieties can you have?
Make a tree diagram.
Suppose you had 20 toppings to choose from. A tree diagram becomes a little cumbersome.
Fundamental Counting Principle – number of ways event #1 can happen times #of ways event #2 can
happen times # of ways event #3 can happen, and so on.
Pizza = Crust Type · Toppings
Instead of tree diagram:
Ex 2: In Penncrest, there are 273 freshman, 291 sophomores, 252 juniors, and 237 seniors. How many
different ways can a committee of 1 freshman, 1 sophomore, 1 junior, and 1 senior be formed?
Ex 3: A multiple choice test has 10 questions with 4 answer choices for each question. In how many
ways could you complete the test?
Ex 4: PA license plates consist of 3 letters followed by 4 numbers. How many license plates can be
created? How many plates can be created if the numbers and the letters cannot repeat?
Permutations – an ordering of a certain number of objects. Permutations can often be used to solve
problems that involve the fundamental counting principle.
Ex: How many ways can A, B, and C be ordered?
ABC ACB BAC BCA CAB CBA
6 ways
--OR-- __________ · ___________ · ____________
# of choices
# of choices
# of choices
st
nd
for 1 spot
for 2 spot
for 3rd spot
Factorial --
n ! = n · (n – 1) · (n – 2) · (n – 3) . . . · 3 · 2 · 1
Ex: 10 ! =
Ex: How many ways can 6 swimmers finish a race?
Ex: How many ways can 6 swimmers finish in 1st, 2nd, or 3rd place?
--OR-- Use Permutation Formula
n
Pr =
n!
( n − r )!
n = total number of objects
r = number in subgroup
n
Pr in calculator.
type in “n” value first.
MATH → PRB
2: n Pr ENTER
type in “r” value
ENTER
Assign p. 705 #15 – 18, 19, 21, 23 – 30, 31 – 37 Odd