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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 5 of 12

Explore more Topics under Discrete Mathematics

Q41.
There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

a.

7! * 6

b.

⁷C₅

c.

7!

d.

same area

Discuss
Answer: (d).same area
Q42.
There are 2 twin sisters among a group of 15 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two sisters?

a.

15 *12! * 2!

b.

15! * 2!

c.

¹⁴C₂

d.

16 * 15!

Discuss
Answer: (a).15 *12! * 2!
Q43.
The number of words of 4 consonants and 3 vowels can be made from 15 consonants and 5 vowels, if all the letters are different is ________

a.

3! * ¹²C₅

b.

¹⁶C₄ * ⁴C₄

c.

15! * 4

d.

¹⁵C₄ * ⁵C₃ * 7!

Discuss
Answer: (d).¹⁵C₄ * ⁵C₃ * 7!
Q44.
How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits?

a.

52347

b.

50388

c.

87658

d.

24976

Discuss
Answer: (b).50388
Q45.
If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d, e) possible such that a+b+c+d+e=75.

a.

⁶⁵C₅

b.

⁵⁸C₆

c.

⁷²C₇

d.

⁷⁴C₄

Discuss
Answer: (d).⁷⁴C₄
Q46.
There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4?

a.

846

b.

2468

c.

658

d.

1317

Discuss
Answer: (d).1317
Q47.
There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together.

a.

876

b.

480

c.

654

d.

237

Discuss
Answer: (b).480
Q48.
How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries?

a.

6

b.

45

c.

12

d.

76

Discuss
Answer: (a).6
Q49.
Find the number of factors of the product 5⁸ * 7⁵ * 2³ which are perfect squares.

a.

47

b.

30

c.

65

d.

19

Discuss
Answer: (b).30
Q50.
From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?

a.

686

b.

438

c.

732

d.

549

Discuss
Answer: (a).686
Page 5 of 12

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