Algebra II
Notes 3.3 The Counting Principle
Number of Ways a Multipart Event Can Happen = number of ways each individual parts can happen.
EX: A restaurant has 2 choices of appetizers, 3 main courses, and 4 desserts. How many different 3course meals can be made?
In above example, you could also make a tree diagram.
Factorial Notation = 4! = 4 x 3 x 2 x 1 = 24.
In calculator: type in n value
MATH
PRB
4: !
EX: How many ways can 5 books be arranged on a shelf?
EX: Find the value of
8!
=
4!
Notes 3.13 Methods of Counting
Permutations – the number of ways a certain number of objects can be arranged when the order of
arrangement matters.
n
Pr =
n!
where n is the total number of objects and r is the number for the subset.
(n − r ) !
In calculator: type in n value
MATH
PRB
2: nPr
type in r value.
EX: How many 3-digit numbers can be created using the numbers 2, 3, 4, 5, 6 if the digits CANNOT
be repeated?
Combinations – the number of ways n objects can be arranged if order does NOT matter.
n
Cr =
n!
where n is the total number of objects and r is the number for the subset.
r !⋅ (n − r )!
In calculator: type in n value
MATH
PRB
3: nCr
type in r value.
EX: How many 3-topping pizzas can be created from 8 different topping choices?