This exercise focuses on combinations, which is the selection of objects where the order does not matter. The formula for the number of combinations of $n$ distinct objects taken $r$ at a time is $C(n, r) = \frac{n!}{r!(n-r)!}$. 1. If $C(n, 8) = C(n, 2)$, find $C(n, 2)$. We use the property that if $C(n, … Read more
This exercise focuses on permutations, which is the arrangement of objects where the order matters. The formula for the number of permutations of $n$ distinct objects taken $r$ at a time is $P(n, r) = \frac{n!}{(n-r)!}$. 1. 3-Digit Numbers from Digits 1 to 9 (No Repetition) We have $n=9$ digits and we are choosing and … Read more
Get detailed, step-by-step solutions for NCERT Class 11 Maths Chapter 6 Exercise 6.2 . Learn to evaluate and simplify expressions involving factorials (e.g., $8!$, $4! – 3!$). Practice algebraic simplification techniques for fractions of factorials, such as $\frac{8!}{6! 2!}$, by expanding the larger factorials. Solve linear equations involving factorials to find the unknown variable $\mathbf{x}$ … Read more
This exercise uses the Fundamental Principle of Counting (Multiplication Principle), where the total number of ways to perform a sequence of independent tasks is the product of the number of ways to perform each task. Class 11 Maths Exercise 6.1 Solutions: Counting Principles, Permutations & Combinations 1. 3-Digit Numbers from Digits 1, 2, 3, 4, … Read more
This exercise combines the concepts of combinations (selection) and permutations (arrangement) to solve various counting problems, including those with constraints. 1. Words with 2 Vowels and 3 Consonants from DAUGHTER The word DAUGHTER has 8 distinct letters. 2. Arrangement of EQUATION where Vowels and Consonants occur together The word EQUATION has 8 distinct letters. The … Read more