Counting Principles

1. What is 7!

7*6*5*4*3*2*1 = 5040

2. Which counting method do you use when order matters, a permutation or a combination?

3. Which is a larger number, or ?

4. What is = 7*6*5 = 210

5. What is =7*6*5/(3*2*1) = 210/6 =35

rnP rnC

?37P

?37C

Counting Principles

6. Seven people are in a race. How many ways can they finish 1st, 2nd and 3rd?

=7*6*5 = 210

7. How many ways can you choose a team of three people from a group of seven?

= 35

8. How many ways can you choose four people from a group of seven?

= 35

9. Why are you answers to seven and eight the same?

Choosing 3 “winners” from seven is the same as choosing four “losers”

37P

37C

47C

Counting Principles

You have a Snickers bar, a bag of chips, a Reesy cup, a pack of Nabs and a Moon Pie in your bookbag. You plan to eat one item in each of your next two periods of school. How many ways can you do this? Consider each food different.

= 2025P

Counting Principles

There are 25 desks in Mr. Gillam’s class and he has 28 students. In how many different ways can they sit at a desk if all desks are filled and three student

are left standing ?

5.8 x 1028

There are 25 desks in Mr. Gillam’s class and he has 28 students. How many different ways can you

choose the three students who are left standing?

3276

2528P

328C

Counting Principles

You have to play 10 games of Grand Theft Auto IX: Blythewood to qualify for the tournament next month. You

have 20 evenings left to play, and can play one game an evening. How many different schedules for playing the ten

games are possible?

184756

You and six other people are in a tournament playing the Guitar Zero video game. How many ways can 1st,

second and third place be awarded?

120

1020C

36P

Counting Principles

Bernie Madoff’s answering machine is full with 32 messages. If 32 distinct individuals called him with death threats, how many different orders could the

calls have come in?

32! = 2.63 x 1035

Counting Principles

Seventy-five AIG employees are receiving bonuses. Five of these bonuses are greater than 4 million dollars. How many ways can you select the five

employees to get the five large bonuses from the seventy-five employees.

17259390

If the government chooses three of the five employees in problem number 19 to testify at a congressional hearing, how many permutations of the order of the

three testimonies are possible?

60

575C

35P

Counting Principles

How many different arrangements are there of the letters in the word NERDY if repetition is

not allowed?

5*4*3*2*1 =

Which of the following is equivalent to n!?

a) b) c) d) 4235P

1Pn

nnP nnC