Sr.Teacher Grade II RPSC PERMUTATIONS AND COMBINATIONS

गणित MATHEMATICS Study Material for Examination for the post of Sr.Teacher Grade II RPSC Gyanpoints +91 9461891001 PERMUTATIONS AND COMBINATIONS Derivation of formulae, their connections and simple applications. BINOMIAL THEOREM Binomial theorem for positive integral indices, general and middle terms in binomial expansion. क्रमचय एवं संचय (Permutations and Combinations) 1. परिचय (Introduction) (i) क्रमगुणित संकेतन (Factorial Notation) प्रथम \(n\) प्राकृत संख्याओं का सतत गुणा क्रमगुणित \(n\) कहलाता है और हम इसे संकेत \(n!\) से व्यक्त करते हैं, इस प्रकार \[ n! = 1 \cdot 2 \cdot 3 \dots (n - 1)n \quad \text{or} \quad n! = n \cdot (n - 1) \cdot (n - 2) \dots 3 \cdot 2 \cdot 1 \] \[ n! = n(n - 1)! = n(n - 1)(n - 2)! = n(n - 1)(n - 2)(n - 3)! \] (ii) उपयोगी परिणाम (Useful results) \(0! = 1\), \(1! = 1\), \(2! = 2\), \(3! = 6\), \(4! = 24\), \(5! = 120\), \(6! = 720\), \(7! = 5040\), \(8! = 40320\), \(9! = 362880\), \(10! = 3628800\) \((-n)! = -\infty\), when \(n\) is an even integer (ज…