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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 4 of 12

Explore more Topics under Discrete Mathematics

Q31.
In a playground, 3 sisters and 8 other girls are playing together. In a particular game, how many ways can all the girls be seated in a circular order so that the three sisters are not seated together?

a.

457993

b.

3386880

c.

6544873

d.

56549

Discuss
Answer: (b).3386880
Q32.
How many numbers of three digits can be formed with digits 1, 3, 5, 7 and 9?

a.

983

b.

120

c.

345

d.

5430

Discuss
Answer: (b).120
Q33.
The size of a multiset is 6 which is equal to the number of elements in it with counting repetitions (a multiset is an unordered collection of elements where the elements may repeat any number of times). Determine the number of multisets can be grouped from n distinct elements so that at least one element occurs exactly twice?

a.

326

b.

28

c.

45

d.

62

Discuss
Answer: (c).45
Q34.
How many words can be formed with the letters of the word ‘CASTLE’ when ‘O’ and ‘A’ occupying end places.

a.

217

b.

48

c.

75

d.

186

Discuss
Answer: (b).48
Q35.
Determine the number of ways of choosing a cricket team (consists of 11 players) out of 18 players if a particular player is never chosen.

a.

12798

b.

22800

c.

31824

d.

43290

Discuss
Answer: (c).31824
Q36.
How many different choices can be made from 5 roses, 4 marigold and 8 sunflowers if at least one flower is to be chosen for making of garland?

a.

269

b.

270

c.

281

d.

320

Discuss
Answer: (a).269
Q37.
In how many ways 6 pens can be selected from 15 identical black pens?

a.

9*3!

b.

21

c.

14!

d.

1

Discuss
Answer: (d).1
Q38.
Determine the number of ways of selecting one or more letters from the letters BBBBBB?

a.

6

b.

73

c.

23

d.

56

Discuss
Answer: (a).6
Q39.
Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women are seated together.

a.

654870

b.

144521

c.

362160

d.

5634

Discuss
Answer: (c).362160
Q40.
Find the number of ways in which 4 people E, F, G, H, A, C can be seated at a round table, such that E and F must always sit together.

a.

32

b.

290

c.

124

d.

48

Discuss
Answer: (d).48
Page 4 of 12

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