Free Practice Quiz Question List

06 Fundamental Counting Principles Online Quiz Questions

Use this free practice quiz with 20 questions to review 06 Fundamental Counting Principles, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A student has 3 shirts and 4 pairs of trousers. If one shirt and one pair of trousers are selected, how many outfits are possible?

A
7
B
12
C
16
D
24

Choose one

1 point

Four distinct tasks must be scheduled one after another, with every task scheduled exactly once. How many schedules are possible?

A
8
B
16
C
24
D
32

Choose one

1 point

Nine members are available for three distinct offices: president, secretary, and treasurer. In how many ways can the offices be assigned if no member holds more than one office?

A
84
B
168
C
336
D
504

Choose all

1 point

Select all statements that correctly describe the addition principle.

A
It applies to mutually exclusive cases.
B
It adds the counts for the separate cases.
C
It is used whenever choices are made in sequence.
D
It requires every case to overlap with every other case.

Choose all

1 point

Select all methods that are identified in the material as useful for handling counting restrictions.

A
Reduce the available choices after each selection when repetition is forbidden.
B
Use a complement when counting the forbidden outcomes is easier.
C
Use a block when a required group must stay together.
D
Use inclusion–exclusion whenever all cases are mutually exclusive.

True or false

1 point

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

A
True
B
False

True or false

1 point

True or false: If 25 students are distributed among 6 discussion groups, at least one group must contain at least 5 students.

A
True
B
False

Written response

1 point

How many ordered selections of 3 distinct objects can be made from 8 distinct objects? Enter the number of selections.

Written response

1 point

What principle is used to count outcomes in overlapping cases by adding the individual counts and subtracting the overlap? Enter the principle's name.

Fill in the blank

1 point

For $n$ distinct objects arranged in a line, the number of arrangements is , and each arrangement is a .

Fill in the blank

1 point

If $n$ objects are distributed among $m$ boxes, some box contains at least objects by the .

Open ended

1 point

A committee of 4 is chosen from 6 engineers and 5 designers. How many committees contain at least one designer? Explain a counting method and justify each step.

Choose one

1 point

Which statement correctly applies the symmetry identity for binomial coefficients?

A
$\binom{9}{2}=28$
B
$\binom{9}{2}=\binom{9}{7}=36$
C
$\binom{9}{2}=\binom{9}{6}=84$
D
$\binom{9}{2}=72$

Choose one

1 point

A café offers 3 soups and 4 sandwiches. A meal consists of one soup and one sandwich. How many different meals can be formed?

A
7
B
12
C
16
D
24

Choose one

1 point

How many ways can 5 distinct books be arranged in a single row?

A
25
B
60
C
120
D
625

Choose one

1 point

A club has 8 members. In how many ways can it choose a president, a vice president, and a secretary, with no member holding more than one office?

A
56
B
112
C
168
D
336

Choose one

1 point

How many different 4-person committees can be selected from 12 people?

A
48
B
495
C
1188
D
20736

True or false

1 point

True or false: If 25 students are assigned to 6 discussion groups, the generalized pigeonhole principle guarantees that at least one group contains at least 4 students.

A
True
B
False

Written response

1 point

How many 5-digit codes can be formed from the digits 0 through 9 if no digit repeats and the first digit cannot be 0? Enter the number of codes as a whole number.

Written response

1 point

What principle counts outcomes in overlapping cases by adding the case counts and subtracting their overlap? Enter the principle's name.