Q. A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
A.
17576
B.
15600
C.
13000
D.
12000
Solution
There are 26 choices for each letter (3 letters) and 10 choices for the first digit and 9 for the second. Total = 26^3 * 10 * 9 = 17576.
Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 3 letters of the alphabet and the first 5 digits?
A.
150
B.
180
C.
120
D.
100
Solution
The number of ways to choose 3 letters from 3 is 3! and 2 digits from 5 is 5P2. Total = 3! * 5P2 = 6 * 20 = 120.
Permutation and Combination are fundamental concepts in mathematics that play a crucial role in various competitive exams and school assessments. Mastering these topics can significantly enhance your problem-solving skills and boost your confidence in tackling objective questions. By practicing MCQs and important questions, you can improve your exam preparation and increase your chances of scoring better.
What You Will Practise Here
Understanding the basic definitions of Permutation and Combination.
Key formulas for calculating permutations and combinations.
Real-life applications of Permutation and Combination concepts.
Solving complex problems using the fundamental counting principle.
Identifying and applying different types of combinations in various scenarios.
Practice questions that cover a range of difficulty levels.
Diagrams and visual aids to clarify concepts and enhance understanding.
Exam Relevance
Permutation and Combination are essential topics in the curriculum for CBSE, State Boards, NEET, and JEE. These concepts frequently appear in various formats, including direct questions, application-based problems, and theoretical explanations. Students can expect to encounter questions that require them to calculate arrangements, selections, and combinations in both objective and subjective formats. Familiarity with these patterns will help you tackle the exam with greater ease.
Common Mistakes Students Make
Confusing between permutations and combinations, especially in word problems.
Neglecting to consider the order of selection when solving permutation problems.
Overlooking the importance of factorial notation in calculations.
Misapplying formulas due to misunderstanding the problem context.
Failing to simplify answers correctly, leading to avoidable mistakes.
FAQs
Question: What is the difference between Permutation and Combination? Answer: Permutation refers to the arrangement of items where order matters, while Combination refers to the selection of items where order does not matter.
Question: How can I improve my skills in Permutation and Combination? Answer: Regular practice of MCQs and objective questions, along with understanding the underlying concepts, will enhance your skills significantly.
Start solving practice MCQs on Permutation and Combination today to solidify your understanding and prepare effectively for your exams. The more you practice, the better you will perform!
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