TOPICS
Introduction
Multiplication Principle or Fundamental Principle of Counting

If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m × n.

Permutations

A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.

Permutations when all the objects are distinct

The number of permutations of n different objects taken r at a time, where 0 < r ≤ n and the objects do not repeat is n ( n – 1) ( n – 2). . .( n – r + 1), which is denoted by ⁿPᵣ.

Factorial notation

The notation n! represents the product of first n natural numbers, i.e., the product 1 × 2 × 3 × . . . × (n – 1) × n is denoted as n!. We read this symbol as ‘n factorial’. Thus, 1 × 2 × 3 × 4 . . . × (n – 1) × n = n !

Derivation of the formula for ⁿPᵣ

The number of permutations of n different things taken r at a time, where repetition is not allowed, is denoted by ⁿPᵣpermutation

Combinations

The formula for finding the number of combinations of n different objects taken r at a time, denoted by ⁿCᵣcombination

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