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Welcome to the Counting Theory MCQs Page

Dive deep into the fascinating world of Counting Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Counting Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Counting Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Counting Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Counting Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Counting Theory MCQs | Page 9 of 12

Explore more Topics under Discrete Mathematics

Q81.
Determine the number of derangements of (2, 4, 6, 1, 3, 5) that end with integer 2, 4 and 6 in some order?

a.

128

b.

29

c.

54

d.

36

Discuss
Answer: (d).36
Q82.
A nursery teacher has 5 pencil boxes to give out to her five students. Determine the probability that at least one student gets their name tag?

a.

19/30

b.

26/47

c.

123/537

d.

12/79

Discuss
Answer: (a).19/30
Q83.
Farhan has received 9 gifts from 9 different people. In how many ways can Farhan receives the gifts such that no one gives him real gifts?

a.

133496

b.

326654

c.

218744

d.

745331

Discuss
Answer: (a).133496
Q84.
There are 7 groups in a picnic who has brought their own lunch box, and then the 7 lunch box are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their own.

a.

655

b.

328

c.

1854

d.

3765

Discuss
Answer: (c).1854
Q85.
Computational complexity of derangements is of __________

a.

NP-complete

b.

NP-hard

c.

NP

d.

P

Discuss
Answer: (a).NP-complete
Q86.
There are 5 different-colored boxes in a room each with a distinct cover. Find out the number of ways so that these covers can be put on the boxes such that none of the boxes can have right covers on it? (Assume that all the covers must be on the boxes).

a.

208

b.

137

c.

239

d.

24

Discuss
Answer: (d).24
Q87.
A postman can put 12 letters into their respective envelopes such that exactly 5 will go into the right envelope. Find the number of ways of doing this work.

a.

2984300

b.

1610496

c.

5322167

d.

3768650

Discuss
Answer: (b).1610496
Q88.
Determine the number of ways In a single competition a singing couple from 5 boys and 5 girls can be formed so that no girl can sing a song with their respective boy?

a.

123

b.

44

c.

320

d.

21

Discuss
Answer: (b).44
Q89.
What is the sum of all 6 digit numbers which can be formed using the digits 2, 3, 5, 6 and 9 exactly once?

a.

986546600

b.

25611866

c.

433338798

d.

319999680

Discuss
Answer: (d).319999680
Q90.
Determine the average of all four digit numbers that can be made using all the digits 2, 3, 5, 7 and 11 exactly once?

a.

3993

b.

1555

c.

5486

d.

1347

Discuss
Answer: (b).1555
Page 9 of 12

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