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.
PermutationsA 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 distinctThe 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 notationThe 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 nPr
The formula for finding the number of combinations of n different objects taken r at a time, denoted by nCr