Topic 3: Counting Principle (All assignments)
Quiz by Fred Spies
Feel free to use or edit a copy
includes Teacher and Student dashboards
Measure skillsfrom any curriculum
Tag the questions with any skills you have. Your dashboard will track each student's mastery of each skill.
- edit the questions
- save a copy for later
- start a class game
- automatically assign follow-up activities based on students’ scores
- assign as homework
- share a link with colleagues
- print as a bubble sheet
- Q1
A family of 6 line up for a family photograph. How many ways are there if the father and mother are at opposite ends of the line?
720 ways
240 ways
24 ways
48 ways
300s - Q2
You are framing a painting. The frames are available in 10 different styles. Each style is 15 different colors. You also want a yellow mat board, which is available in 5 different shades of yellow. How many ways can you frame a painting?
30
750
75
1500
300s - Q3
There are 5 roads leading to a town from a village. What is the number of different ways in which a villager can go to the town and return back?
20
None of the above
10
5
300s - Q4
A school has different course offerings: 4 in languages, 6 in mathematics, 5 in social studies, and 3 in science. How many different 4-course student schedules are possible if a student must have one course from each subject area?
24
360
120
4
300s - Q5
In an examination, there are five multiple-choice questions and each question has 4 choices. How many ways can a student fail to get all answers correct?
1023
19
624
20
300s - Q6
How many different ways can the letters of "PIZZERIA" be arranged?
40,320
10,080
5040
720
300s - Q7
What is the number of distinguishable permutations of the letters in the word “HAWAII”?
24
180
720
360
300s - Q8
Morse code is a system of dots, dashes, and spaces that telegraphers once used to send messages by wire. How many different arrangements are there of 2 dashes, 2 spaces, and 5 dots? (Hint: Distinguishable permutations)
756
362,880
40,320
20
300s - Q9
The board of directors is composed of 10 members. In how many ways can they elect a chairperson, vice-chairperson, treasurer, and secretary, assuming that one person cannot hold more than one office?
210
720
24
5,040
300s - Q10
Three couples have reserved seats for a Broadway musical. How many different ways can they sit if two members of each couple wish to sit together?
24
2
720
48
300s - Q11
How many different ways can 5 paintings be displayed on a wall?
720
15
120
24
300s - Q12
How many arrangements if a waiter places 5 drinks along the edge of a circular tray?
120
720
60
24
300s - Q13
Suppose 7 points on the circle are selected at random. Relative to the point which lies on the x-axis, how many arrangements are possible?
40,320
2,520
720
5,040
300s - Q14
What is 16C3?
680
560
3,360
433
300s - Q15
You are required to answer 12 out of 15 questions in an examination such that you must choose 5 from the first six questions, and the rest from the next 9 questions. How many choices are available to you?
455
300
216
126
300s
