Lesson 8-2

Example 1 Find a Permutation
FOOD A pizza place offers 12 different toppings. Jack wants to buy a three-topping pizza. How many pizzas can he buy if order is important?

number of possible toppings available		number of possible toppings available after the first topping is chosen		number of possible toppings available after the second topping is chosen	=	total number of possible pizzas with 3 toppings	

12		11		10	=	1,320	

There are 1,320 different pizzas Jack can order.

Example 2 Use Permutation Notation
Find P(7, 3).

P(7, 3) = 7 · 6 · 5 or 210	7 things taken 3 at a time.

Example 3 Use Permutation Notation
Find P(5, 5).

P(5, 5) = 5 · 4 · 3 · 2 · 1 or 120	5 things taken 5 at a time.

Example 4 Find Probability
NUMBERS Consider all of the three-digit numbers that can be formed using the digits 1, 2, and 3 where no digit is used twice. Find the probability that one of these numbers picked at random is between 200 and 300.

You are considering all permutations of 3 digits taken 3 at a time. You wish to find the probability that one of these numbers picked at random is greater than 200 but less than 300.

Find the number of possible three-digit numbers.
P(3, 3) = 3!

For a number to be between 200 and 300, the hundreds digit must be 2.

number of ways to pick the first digit		number of ways to pick the last two digits	=	number of permutations between 200 and 300	

1		P(2, 2)	=	P(2, 2) or 2!	

P(between 200 and 300) = 
	= 	Substitute.
	= 	Divide out common factors.
	=  or 33%	Simplify.