Free Printable 3.4 Additional Topics in Probability and Counting

Worksheets

3.4 Additional Topics in Probability and Counting

Total questions: 25

Worksheet time: 6hrs 15mins

Name

Class

Date

Your friends rented 6 different video games.

In how many different orders can you play the 6 games?

720 different orders

120 different orders

36 different orders

46646 different orders

6 different orders

There are 20 games to choose from at the local game store.

How many different sets of 4 games could you choose to rent?

₂₀P₄ = 116280

₂₀C₄ = 4845

$\frac{20!}{4!}=101370917007360000$

16! = 20922789888000

The Smith Family has a garage door that opens with a 4-digit PIN.

They decide to base the code on the birthday of 01/24/36.

How many PINs are there that use four of the digits in the birthday?

₆P₄ = 360

₆C₄ = 15

$\frac{6!}{4!}=30$

6 ⋅ 4 = 24

There are 6 class periods in the school day.

There are 10 subjects to choose from.

How many different class schedules are possible?

₁₀P₆ = 151200

₁₀C₆ = 210

4! = 24

$\frac{10!}{6!}=5040$

6 ⋅ 10 = 60

There are 15 slips of paper in each jar.

Each slip has a different name on it.

How many ways can you draw 5 names from the jar?

₁₅P₅ = 360360

₁₅C₅ = 3003

12! = 479001600

15 ⋅ 5 = 75

$\frac{15!}{5!}=19897286400$

There are 30 songs on your music player.

In how many different ways can you arrange 20 songs to listen to while exercising?

₃₀P₂₀ = 73096577329197271449600000

₃₀C₂₀ = 30045015

10! = 3628800

30 ⋅ 20 = 600

$\frac{30!}{20!}=109027350432000$

The football team will select 5 captains from their seniors.

There are 15 seniors on the team.

How many different groups of captains could be selected?

₁₅P₅ = 360360

₁₅C₅ = 3003

3! = 6

$\frac{15!}{5!}=10897286400$

15 ⋅ 5 = 75

There are 8 finalists in the spelling bee.

The order of the contestants will be determined by a random draw.

How many different orders are possible for the final spelling bee?

40320

A restaurant's menu offers 8 different sandwiches and 5 side dishes. How many lunch menu combinations can you order?

₈P₅ = 6720

₈C₅ = 56

3! = 6

$\frac{8!}{5!}=336$

8 ⋅ 5 = 40

10.

A full house consists of three of one kind and two of another kind.

Set up the calculation to find the probability of being dealt a full house consisting of three kings and two queens.

11.

A security code consists of three letters followed by one digit.

The first letter cannot be an A, B, or C.

How many different security codes can be generated?

149500

156000

155480

134550

139932

12.

A batch of 200 calculators contains 3 defective units.

0.955451 is the approximate probability that a sample of three calculators will have:

no defective calculators

all defective calculators

at least one defective calculator

at least one nondefective calculator

no more than one defective calculator

13.

A batch of 350 raffle tickets contains four winning tickets.

You buy four tickets.

0.954873 is the approximate probability that you have:

no winning tickets

all of the winning tickets

at least one winning ticket

at least one non-winning ticket

only one winning ticket

14.

A corporation has six male senior executives and four female senior executives.

Four senior executives are chosen at random to attend a technology seminar.

Find the approximate probability of choosing:

four men

0.071429

four women

0.004762

two men and two women

0.428571

one man and three women

0.114286

15.

A florist has 12 different flowers from which floral arrangements can be made.

If a centerpiece is to be made using four different flowers, how many different arrangements can be made?

₁₂P₄ = 11880

₁₂C₄ = 495

$\frac{12!}{4!}=\ 19958400$

8! = 40320

16.

From a pool of 16 candidates, 9 men and 7 women, the offices of President, Vice President, Secretary, and Treasurer will be filled.

In how many different ways can the offices be filled?

₁₆P₄ = 43680

₁₆C₄ = 1820

$\frac{16!}{4!}=871782912000$

12! = 479001600

17.

At Papa John's, you are deciding on what you want for dinner.

The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces.

How many different pizzas do you have to choose from?

192

40,320

51,200

30630600

18.

What does ₁₀P₅mean?

Permutations with 5 choices and 10 positions

Permutations with 10 choices and 5 positions

Permutations with 5 numbers and 10 operations

Permutations with 5 hot dogs and 10 drinks

Permutations of 10 flowers with 5 types of flowers

19.

How many ways can you choose a manager and assistant from a 9-person task force?

20.

There are 7 students in a class: 5 boys and 2 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

$\frac{5}{7}$

$\frac{1}{7}$

$\frac{2}{7}$

$\frac{4}{7}$

21.

How many distinguishable ways can you arrange the letters in the word finite?

336

720

360

22.

There are 18 people running in a cross country race.

How many possible ways are there to place the runners in first, second, and third?

₁₈P₃ = 4896

₁₈C₃ = 816

$\frac{18!}{3!}=\ 1067062284288000$

15! = 1307674368000

6! = 720

23.

If you roll a die then flip a coin, how many possible outcomes?

24.

You flip a nickel three times.

Find the probability that all flips will land on tails.

⅙

⅛

25.

A lock has four dials. On each dial are the digits 0 to 9.

How many possible combinations are there if you cannot reuse a number?

5040

6561

10,000

100 %

3.4 Additional Topics in Probability and Counting

Total questions: 25

Worksheet time: 6hrs 15mins

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