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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 3 of 12

Explore more Topics under Discrete Mathematics

Q21.
A bag contains 25 balls such as 10 balls are red, 7 are white and 8 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

a.

10

b.

18

c.

63

d.

35

Discuss
Answer: (b).18
Q22.
How many substrings (of all lengths inclusive) can be formed from a character string of length 8? (Assume all characters to be distinct)

a.

14

b.

21

c.

54

d.

37

Discuss
Answer: (d).37
Q23.
The number of diagonals can be drawn in a hexagon is ______

a.

9

b.

32

c.

16

d.

21

Discuss
Answer: (a).9
Q24.
The number of binary strings of 17 zeros and 8 ones in which no two ones are adjacent is ___________

a.

43758

b.

24310

c.

32654

d.

29803

Discuss
Answer: (a).43758
Q25.
How many words that can be formed with the letters of the word ‘SWIMMING’ such that the vowels do not come together? Assume that words are of with or without meaning.

a.

430

b.

623

c.

729

d.

1239

Discuss
Answer: (c).729
Q26.
A number lock contains 6 digits. How many different zip codes can be made with the digits 0–9 if repetition of the digits is allowed upto 3 digits from the beginning and the first digit is not 0?

a.

254307

b.

453600

c.

458760

d.

972340

Discuss
Answer: (b).453600
Q27.
Let M be a sequence of 9 distinct integers sorted in ascending order. How many distinct pairs of sequences, N and O are there such that i) each are sorted in ascending order, ii) N has 5 and O has 4 elements, and iii) the result of merging N and O gives that sequence?

a.

84

b.

35

c.

194

d.

138

Discuss
Answer: (a).84
Q28.
14 different letters of alphabet are given, words with 6 letters are formed from these given letters. How many number of words are there which have at least one letter repeated?

a.

892742

b.

999988

c.

213216

d.

786730

Discuss
Answer: (b).999988
Q29.
In how many ways can 10 boys be seated in a row having 28 seats such that no two friends occupy adjacent seats?

a.

¹³P₅

b.

⁹P₂₉

c.

¹⁹P₁₀

d.

¹⁵P₇

Discuss
Answer: (c).¹⁹P₁₀
Q30.
How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes?

a.

40325

b.

40320

c.

40520

d.

40720

Discuss
Answer: (b).40320
Page 3 of 12

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