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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 7 of 12

Explore more Topics under Discrete Mathematics

Q61.
For a gaming competition, 8 girls are planning on splitting up into 3 (non-empty) groups. How many ways can they split up into these groups?

a.

465

b.

1056

c.

966

d.

3215

Discuss
Answer: (c).966
Q62.
In a picnic with 20 persons where 6 chocolates will be given to the top 8 children(the chocolates are distinct: first, second). How many ways can this be done?

a.

¹⁸C₆

b.

²⁰P₆

c.

²⁵C₄ * 6!

d.

¹⁹P5

Discuss
Answer: (b).²⁰P₆
Q63.
How many ways can one choose 20 cookies from 45 different types (assuming there are at least 20 of each type)?

a.

⁶⁴C₂₁ * 15

b.

⁶⁴C₂₀

c.

⁴⁴C₂₀ * 2!

d.

⁶⁵C₂₂

Discuss
Answer: (b).⁶⁴C₂₀
Q64.
Assume that it is an afternoon. What is the time on the 24 hour clock after 146 hours?

a.

12:10 pm

b.

8:30 am

c.

3 am

d.

2 pm

Discuss
Answer: (d).2 pm
Q65.
There are 28 identical oranges that are to be distributed among 8 distinct girls. How many ways are there to distribute the oranges?

a.

²²P₇

b.

³⁴C₆

c.

³⁵C₇

d.

²⁸C₈

Discuss
Answer: (c).³⁵C₇
Q66.
There are 5 distinct fruits. How many ways can they be planted into identical fruit plants?

a.

87

b.

52

c.

76

d.

128

Discuss
Answer: (b).52
Q67.
A woman has 14 identical pens to distribute among a group of 10 distinct students. How many ways are there to distribute the 14 pens such that each student gets at least one pencil?

a.

¹⁵C₁₀

b.

¹⁰C₅ * 11

c.

¹⁵C₈ * 4!

d.

¹³C₉

Discuss
Answer: (d).¹³C₉
Q68.
Suppose that M is the product of k distinct primes. Find the number of ways to write N as the product of positive integers(>1), where the order of terms does not matter.

a.

ᴹCₙ₋ₖ

b.

ᴺCₘ

c.

N * Bₖ

d.

Bᴋ

Discuss
Answer: (d).Bᴋ
Q69.
How many ways are there to place 7 differently colored toys into 5 identical urns if the urns can be empty? Note that all balls have to be used.

a.

320

b.

438

c.

1287

d.

855

Discuss
Answer: (d).855
Q70.
Suppose, there are 7 of your friends who want to eat pizza (8 distinct people in total). You order a 16-cut pizza (16 identical slices). How many distributions of pizza slices are there if each person gets at least one slice of pizza?

a.

346

b.

6435

c.

3214

d.

765

Discuss
Answer: (b).6435
Page 7 of 12

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