Fundamental Principle of Counting Quiz - CBSE Class 11 Mathematics

Free practice quiz: Fundamental Principle of Counting (CBSE Class 11 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 11 Mathematics practice quiz has 16 multiple-choice questions on Fundamental Principle of Counting, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. A restaurant offers 3 appetizers, 5 main courses, and 2 desserts. How many different three-course meals are possible?

   1. 10
   2. 15
   3. 30
   4. 100
   Show answer

   Answer: C. 30

   Using the fundamental principle of counting, multiply the number of choices for each course: 3 * 5 * 2 = 30.

2. How many three-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition is not allowed?

   1. 10
   2. 60
   3. 120
   4. 125
   Show answer

   Answer: B. 60

   For the hundreds place, there are 5 choices. For the tens place, there are 4 remaining choices. For the units place, there are 3 remaining choices. Therefore, the total number of three-digit numbers is 5 * 4 * 3 = 60.

3. How many different ways can you arrange the letters in the word 'MATH'?

   1. 12
   2. 24
   3. 120
   4. 240
   Show answer

   Answer: B. 24

   This is a permutation problem. There are 4 letters, so there are 4! = 4 * 3 * 2 * 1 = 24 ways to arrange them.

4. How many 4-digit numbers can be formed using digits 1,2,3,4,5,6 if repetition is allowed?

   1. 36
   2. 1296
   3. 216
   4. 720
   Show answer

   Answer: B. 1296

   Since repetition is allowed, each of the four places can have 6 options. Therefore 6*6*6*6 = 1296.

5. A bag contains 5 red balls and 3 blue balls. In how many ways can you select 2 red balls and 1 blue ball?

   1. 10
   2. 30
   3. 15
   4. 60
   Show answer

   Answer: B. 30

   The number of ways to choose 2 red balls from 5 is 5C2 = 10. The number of ways to choose 1 blue ball from 3 is 3C1 = 3. The total number of ways is 10 * 3 = 30.

More questions in this quiz

Answers and explanations are in the full quiz.

1. A student has 4 shirts, 3 pants, and 2 pairs of shoes. How many different outfits can they wear?
2. A license plate has 3 letters followed by 2 digits. How many different license plates are possible if repetition is allowed?
3. A coin is tossed 4 times. How many different outcomes are possible?
4. A die is rolled three times. How many possible outcomes are there?
5. A committee of 3 people is to be selected from a group of 6 people. How many different committees are possible?
6. In how many ways can 5 different books be arranged on a shelf?
7. A password must be 8 characters long and contain only lowercase letters. How many possible passwords are there?
8. How many permutations are there of the letters in the word 'MISSISSIPPI'?
9. There are 7 points in a plane, no three of which are collinear. How many triangles can be formed using these points?
10. How many ways can you arrange the letters of the word 'STATISTICS' such that the vowels are always together?
11. In a group of 20 people, what is the probability that at least two people share the same birthday?

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