Permutation and Combination

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Permutation and Combination MCQ & Objective Questions

Permutation and Combination is a crucial topic in mathematics that plays a significant role in various exams. Mastering this area can greatly enhance your problem-solving skills and boost your confidence. Practicing MCQs and objective questions on Permutation and Combination helps you familiarize yourself with the types of questions asked in exams, ensuring better preparation and higher scores.

What You Will Practise Here

  • Fundamental principles of counting
  • Formulas for permutations and combinations
  • Applications of permutations in real-life scenarios
  • Applications of combinations in probability
  • Common problems involving arrangements and selections
  • Understanding factorial notation and its significance
  • Diagrams and visual aids for better comprehension

Exam Relevance

Permutation and Combination is a vital topic in the syllabus of CBSE, State Boards, NEET, and JEE. It frequently appears in various formats, including direct questions, application-based problems, and conceptual MCQs. Students can expect questions that require them to calculate arrangements, selections, or even solve problems involving probability, making it essential to grasp the underlying concepts thoroughly.

Common Mistakes Students Make

  • Confusing permutations with combinations, especially in word problems.
  • Neglecting the importance of order in arrangements.
  • Misapplying formulas due to misunderstanding factorials.
  • Overlooking restrictions or conditions in selection problems.
  • Failing to simplify problems before applying formulas.

FAQs

Question: What is the difference between permutations and combinations?
Answer: Permutations consider the order of selection, while combinations do not. For example, arranging books on a shelf is a permutation, whereas selecting books to read is a combination.

Question: How can I improve my speed in solving Permutation and Combination problems?
Answer: Regular practice with MCQs and objective questions will help you identify patterns and improve your calculation speed.

Start solving practice MCQs on Permutation and Combination today to test your understanding and enhance your exam readiness. Remember, consistent practice is the key to mastering this topic and achieving your academic goals!

Q. How many ways can 6 people be seated in a row if two specific people must sit together?
  • A. 120
  • B. 720
  • C. 600
  • D. 480
Q. How many ways can 7 different books be arranged on a shelf if 2 specific books must be together?
  • A. 720
  • B. 1440
  • C. 5040
  • D. 840
Q. How many ways can a committee of 3 be formed from 10 people?
  • A. 120
  • B. 90
  • C. 100
  • D. 80
Q. How many ways can a committee of 3 be formed from 8 people?
  • A. 56
  • B. 48
  • C. 40
  • D. 36
Q. How many ways can the letters of the word 'BANANA' be arranged?
  • A. 60
  • B. 30
  • C. 20
  • D. 10
Q. How many ways can you arrange the letters of the word 'MATH'?
  • A. 24
  • B. 12
  • C. 16
  • D. 20
Q. How many ways can you choose 2 fruits from 5 different fruits?
  • A. 10
  • B. 5
  • C. 15
  • D. 20
Q. How many ways can you choose 2 toppings from 5 available toppings for a pizza?
  • A. 10
  • B. 15
  • C. 20
  • D. 5
Q. How many ways can you choose 4 cards from a deck of 52 cards?
  • A. 270725
  • B. 1001
  • C. 1300
  • D. 2000
Q. How many ways can you choose 4 students from a class of 12?
  • A. 495
  • B. 300
  • C. 400
  • D. 600
Q. How many ways can you form a committee of 3 from 8 people?
  • A. 56
  • B. 28
  • C. 36
  • D. 48
Q. How many ways can you select 3 out of 7 different colored shirts?
  • A. 35
  • B. 21
  • C. 7
  • D. 14
Q. How many ways can you select 4 cards from a deck of 52 cards?
  • A. 270725
  • B. 130816
  • C. 22100
  • D. 10000
Q. If a committee of 4 is to be formed from 8 people, how many different committees can be formed?
  • A. 70
  • B. 56
  • C. 28
  • D. 36
Q. If a committee of 4 members is to be formed from 8 people, how many different committees can be formed?
  • A. 70
  • B. 56
  • C. 28
  • D. 12
Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 5 letters and 5 digits?
  • A. 2500
  • B. 5000
  • C. 12500
  • D. 15000
Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed?
  • A. 175760
  • B. 456976
  • C. 1000
  • D. 100
Q. In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
  • A. 60
  • B. 40
  • C. 20
  • D. 30
Q. In how many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?
  • A. 100
  • B. 120
  • C. 150
  • D. 200
Q. In how many ways can 2 out of 5 different fruits be selected?
  • A. 10
  • B. 15
  • C. 20
  • D. 5
Q. In how many ways can 3 different prizes be awarded to 5 students?
  • A. 60
  • B. 100
  • C. 30
  • D. 20
Q. In how many ways can 3 different trophies be awarded to 10 students?
  • A. 720
  • B. 1000
  • C. 120
  • D. 300
Q. In how many ways can 3 prizes be distributed among 5 students if each student can win more than one prize?
  • A. 125
  • B. 243
  • C. 1250
  • D. 100
Q. In how many ways can 3 students be selected from a group of 10?
  • A. 120
  • B. 90
  • C. 100
  • D. 80
Q. In how many ways can 4 different books be chosen from a shelf of 10?
  • A. 210
  • B. 120
  • C. 60
  • D. 30
Q. In how many ways can 4 different colored balls be arranged in a row?
  • A. 16
  • B. 24
  • C. 32
  • D. 48
Q. In how many ways can 4 different prizes be awarded to 10 students?
  • A. 5040
  • B. 720
  • C. 100
  • D. 40
Q. In how many ways can 4 people be seated at a round table?
  • A. 24
  • B. 12
  • C. 6
  • D. 4
Q. In how many ways can 5 books be arranged on a shelf?
  • A. 120
  • B. 60
  • C. 24
  • D. 30
Q. In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?
  • A. 48
  • B. 120
  • C. 60
  • D. 24
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