Permutation and Combination Questions For CAT Exam | Day 35

Part-1: Quantitative Aptitude for CAT exam

CAT Exam Important Topic: Strategy to Prepare “Permutations and Combinations (Principle of Counting and Arrangement)” and CAT Permutation and Combination Questions.

Permutation and combination CAT Formula and Concepts:

• Fundamental Principle of Counting
• Rule of Product: Taking 1 out of m objects and taking 1 out of n objects, the total number of ways taking 1 out of each of m and n = m x n
• Rule of Addition: Taking 1 out of m objects or taking 1 out of n objects, the total number of ways taking 1 out of each of either m or n = m + n
• Linear Arrangements: Arranging n objects at n different places = n!
• Circular Arrangements: Arranging n objects at n different places(circularly) = (n-1)!

Permutation and Combination Examples:

Permutation Examples:

1. Arranging Books: You have 4 different books (A, B, C, D) and you want to arrange them on a shelf. The number of ways to arrange them in a specific order would be a permutation. For example, ABCD, ACBD, BCAD, etc.

2. Choosing a Committee: You have 5 people and you want to choose a president, vice-president, and secretary from among them. The order in which you choose these roles matters, so this is a permutation.

Combination Examples:

1. Picking Fruits: You have 6 different fruits and you want to choose 3 to take with you. The order in which you choose them doesn't matter, only which fruits you select. This is a combination.

2. Selecting a Pizza Topping: You are ordering a pizza and can choose 4 toppings from a list of 8. The order in which the toppings are placed on the pizza doesn't matter, so this is a combination.

CAT Exam: Basic Principle of Counting: Permutation And Combination Previous Year Questions

Q1. How many four-digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, and 6, such that no digit is used more than once and 0 does not occur in the left-most position? [TITA, CAT 2017]

Solution:

This CAT Permutation and Combination questions are based on Arrangements

Some points to be noticed: permutation and combination formula -

0 does not occur in the leftmost position.

If the numbers are to be divisible by 6 it should be a multiple of 2 and 3.

So, the number should be an even number and also be divisible by 3.

Permutations and combinations Examples:

At the unit place, there can be either 0, 2, 4, 6

Permutations and combinations Case 1: Unit Place is ‘0’

Sum of the rest of three should be divisible by 3, The possible pairs are

2, 3, 4; Number of arrangements = 3! = 6.

2, 4, 6; Number of arrangements = 3! = 6.

Total Numbers in Case 1 = 12

Permutations and combinations Case 2: Unit Place is ‘2’

Sum of all four digits should be divisible by 3, The possible pairs are

0, 4, 6 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4

3, 4, 6 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.

0, 3, 4 (Sum 0+ 4+ 3+ 2= 9); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4

Total Numbers in Case 2 = 14

Permutations and combinations Case 3: Unit Place is ‘4’

Sum of all four digits should be divisible by 3, The possible pairs are

2, 3, 6 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.

0, 2, 6 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4

0, 3, 2 (Sum 0+ 4+ 3+ 2= 9); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4

Total Numbers in Case 3 = 14

Permutations and combinations Case 4: Unit Place is ‘6’

Sum of all four digits should be divisible by 3, The possible pairs are

2, 3, 4 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.

0, 2, 4 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4

Total Numbers in Case 4 = 10

Therefore, in total we can form 12 + 14 + 14 + 10 = 50 four- digit numbers.

Hence, the answer is 50

Pre-requisite to permutations and combinations for CAT exam

• Vedic Maths

• Factorial

CAT study material: References to Study (Theory) permutations and combinations for CAT exam

• NCERT Class 11 Maths

• CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=kqTIPJQ4JAM)

References to Practice CAT Permutation and Combination Questions

• Practice CAT Permutation and Combination Questions

• How to prepare quantitative Aptitude for CAT by Arun Sharma.

• R B Classes (YouTube, Link: https://www.youtube.com/watch?v=St4IMbF4Kh0)

Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2024 Syllabus Topic: Strategy to prepare “Syllogism” (Part-1)

Important Concepts/ Formulas

The syllogism consists of statements and conclusions.

Some Rules:

1. All+ All=All

2. All+ No=No

3. All+ Some=No conclusion

4. Some+ All=Some

5. Some+ No= Some Not

6. Some+ Some= No Conclusion

7. No+ No=No Conclusion

CAT Exam: CAT Previous Year Questions on Syllogism from CAT/ MBA Entrance Exam:

Q1. The following question is given by 2 statements and 2 conclusions numbered I and II. Choose the right answer from the given options. [CMAT]

Statements:

All huts are bungalows.

All bungalows are churches.

Conclusions:

I. Some churches are huts.

II. Some churches are bungalows.

1. If only conclusion II follows

2. If either conclusion I or II follows

3. If only conclusion I follows

4. If both conclusions I and II follow

Answer: [D]

All + All = All positive conclusions will follow,

Therefore, both I and II will follow.

Q2. If all apples are red, and some apples are juicy, which of the following statements is true? [TISSNET]

1. All apples are juicy.

2. Some juicy apples are red.

3. Some red apples are juicy.

1. First statement

2. Second and Third Statement

3. Third Statement

4. None of the above

Syllogism questions with Answers: B

Clearly, the second and third statements will follow.

CAT entrance exam: Prerequisite to Syllogism

• Set Theory

• Venn Diagram

Tips and Tricks for CAT

• Two types of conclusions are there:

• 
  

  • Definite

  • Possible

• If All A are B; Possibility: Some B is not A.

• If Some B is not A; Possibility: All A are B.

• If Some A are B; Possibility: All A are B; All B is A.

• Consider all the possibilities.

• Questions can be solved by either of the following methods:

• 
  

  • Venn Diagram

  • Analytical Method

• Practice Sample Papers

CAT syllabus 2024: References to Study (Theory) syllogism reasoning

• Verbal and Non-Verbal Reasoning by B S Sijwali

• Feel Free to Learn (YouTube link: https://www.youtube.com/watch?v=ev2SkXJVAbA&list=PLOoogDtEDyvsBG38tzlj1Zkd0PLxgZwXV)

CAT Exam: References to Practise Syllogism

• Verbal and Non-Verbal Reasoning by R S Agrawal.

• CAT Previous years Papers and Sample Papers.

• Ck CetKing (YouTube; Link: https://www.youtube.com/watch?v=uwfrfzhBkus)

Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Parallelism”

CAT Important Basic Concept

Use of the same pattern of words for two or more ideas that have the same level of importance.

CAT Previous Years' Questions on Parallelism

Find the error and correct the sentence

Q1: Most people cope up with anxiety by reaching for food rather then deal with their feelings. {Similar to CAT PYQ]

1. cope up with anxiety by reaching for food rather than deal with their feelings.

2. cope up with anxiety by reaching for food rather than dealing with their feelings.

3. cope with anxiety by reaching for food rather than deal with their feelings.

4. cope with anxiety by reaching for food rather than dealing with their feelings.

Solution: [D]

‘Cope up with' should be replaced with 'cope with'.

'Rather then' should be 'rather than'.

Also, the parallelism error is there; change 'deal' to 'dealing'.

Q2. Ashok is not only a terrific vocalist, but also great at solving mathematics. [Sample Question]

1. Ashok is not only a terrific vocalist, but also great at solving mathematics.

2. Ashok not only is a terrific vocalist, but is also great at solving mathematics.

3. Not only great at solving mathematics, Ashok also is a terrific vocalist.

4. Ashok is not only a terrific vocalist, but also a great mathematician.

5. Also great at solving mathematics, Ashok is a terrific vocalist.

Ans: [D]

Grammar issue presented: Parallelism (correlative pairs)

“Not only…but also” is a correlative pair, so the elements immediately following each conjunction must be parallel.

CAT 2024: Pre-requisite

1. Sentence Structure

2. Conjunction and Prepositions

Tips and Tricks for CAT Exam

1. Know when the parallel structure is required.

2. Put structurally equivalent words or phrases in the same part of speech.

3. Put structurally equivalent verbs in the same form.

4. Use clauses or complete sentences consistently.

5. Avoid faulty parallelism.

CAT exam: References to Study Theory

1. Wren and Martin

2. Rodha (https://www.youtube.com/watch?v=Vnc7Y_l8Hj4)

CAT exam: References to Practice

1. Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.

2. CAT Previous years Papers and Sample Papers.

3. Rodha (youTube; Link: https://www.youtube.com/watch?v=IoZL7ZcuRmQ)

Keep working hard and practicing; Day 36 will be posted tomorrow.

Thank you

All the Best!