Free Practice Quiz Question List

2 Counting Techniques Online Quiz Questions

Use this free practice quiz with 20 questions to review 2 Counting Techniques, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: By definition, $0! = 1$ .

A
True
B
False

Choose one

1 point

Eighteen students study French, 12 study Spanish, and 5 study both. How many students study at least one of the two languages?

A
30
B
35
C
25
D
20

Choose all

1 point

Select all situations that are correctly modeled primarily by the multiplication principle.

A
Choosing one shirt and one pair of pants
B
Creating a password with separate letter and digit positions
C
Choosing one elective from either the art group or the music group
D
Selecting a three-person committee from ten people

True or false

1 point

True or false: When people are assigned to president, vice president, and treasurer, exchanging two people creates a different outcome because the offices are different.

A
True
B
False

Written response

1 point

A password has 2 letters followed by 3 digits. No symbol may repeat. How many such passwords are possible?

Fill in the blank

1 point

Five distinct books are arranged on a shelf. The number of possible arrangements is .

Choose one

1 point

A five-card hand is selected from a standard 52-card deck. Which expression gives the probability that the hand contains exactly two aces?

A
$\frac{\binom{4}{2}+\binom{48}{3}}{\binom{52}{5}}$
B
$\frac{\binom{4}{2}\binom{48}{3}}{\binom{52}{5}}$
C
$\frac{P(4,2)P(48,3)}{P(52,5)}$
D
$\frac{\binom{52}{2}\binom{48}{3}}{\binom{52}{5}}$

Choose all

1 point

Select all statements that are correct about permutations and combinations.

A
A committee selection generally uses a combination because listing order does not matter.
B
Assigning people to distinct offices is an ordered selection.
C
The identity $P(n,r)=\binom{n}{r}r!$ first chooses objects and then arranges them.
D
A combination always means that objects may be selected repeatedly.

True or false

1 point

True or false: When counting possible final five-card hands, the denominator should be $\binom{52}{5}$ because the order of dealing does not change the hand.

A
True
B
False

Written response

1 point

What counting principle is used when a procedure consists of successive stages, with a specified number of choices at each stage?

Fill in the blank

1 point

Complete the relationship between permutations and combinations: $P(n,r)=$ .

Open ended

1 point

A box contains 8 phones, 3 of which are defective. Two phones are selected without replacement. Determine the probability that both selected phones are good, and explain why your numerator and denominator count the appropriate outcomes.

Choose one

1 point

How many distinct arrangements can be made from the letters in LEVEL?

A
10
B
20
C
30
D
60

Choose one

1 point

How many four-digit codes can be formed from the digits 0 through 9 if no digit may repeat, the first digit cannot be 0, and the last digit must be even?

A
2016
B
2176
C
2288
D
2296

Choose one

1 point

What is the value of $0!$ ?

A
$1$
B
$0$
C
$-1$
D
$10$

Choose one

1 point

At a school, 18 students study French, 12 study Spanish, and 5 study both languages. How many students study at least one of the two languages?

A
$30$
B
$35$
C
$25$
D
$20$

Choose one

1 point

A password has 2 letters followed by 3 digits. No symbol may be repeated. How many such passwords are possible?

A
$676{,}000$
B
$520{,}000$
C
$468{,}800$
D
$468{,}000$

Choose one

1 point

Six people are competing for president, vice president, and treasurer. How many different assignments of the three offices are possible?

A
$60$
B
$120$
C
$216$
D
$720$

Written response

1 point

A box contains 8 phones, 3 of which are defective. If 2 phones are selected without replacement, what is the probability that both are good? Enter a reduced fraction.

Written response

1 point

How many distinct arrangements can be made from the letters in LEVEL? Enter the answer as an integer.