Consider the following scenario: You have a bag with a number lock. The number lock comprises four wheels, each with ten digits ranging from 0 to 9. The lock can be opened if four precise digits are put in a specific order with no repeat. You've somehow forgotten this particular numerical sequence. Only the first digit, 7, is remembered. How many 3-digit sequences will you have to e x amine to open the lock? To solve this question, begin by making a list of all conceivable combinations of the 9 remaining digits, three at a time. However, this procedure will be tiresome because the number of alternative sequences is likely to be huge. Permutations and combinations formulas are important for you to understand such concepts.
We'll learn some fundamental counting procedures in this chapter that will allow us to solve this issue without listing 3-digit groupings. Similar methods can be used to determine the number of distinct ways to arrange and pick things without listing them. As a first step, we'll look at a principle that's critical to understanding these strategies. NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations is important to understand as it will help in grasping some basic concepts. You can refer to NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations to get multiple ways of solving a problem.
2. Fundamental Principle of Counting
3.1. Permutations when all the objects are distinct
3.2. Factorial notation
3.3 Derivation of the formula nPr
3.4. Permutations when all the objects are not distinct