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Unit 12: Permutation

ways after Subtask 1 and Subtask 2 have been performed, and so on. Then the multiplication Notes
principle says that the number of ways in which the whole task can be performed is n , n …. n .
1 2 k
Let us consider this principle in the context of boxes and objects filling them. Suppose there are
m boxes. Suppose the first box can be filled up in k(1) ways. For every way of filling the first box,
suppose there are k(2) ways of filling the second box. Then the two boxes can be filled up in k(1),
k(2) ways. In general, if for every way of filling the first (r “ 1) boxes, the rth box can be filled up
in k(r) ways, for r = 2, 3, … m, then the total number of ways of filling all the boxes is k(1), k(2)…
k(m).
So let us see how the multiplication principle can be applied to the situation above (the shop
selling pants). Here k(1) = 6, k(2) = 8, k(3) = 6 and k(4) = 4. So, the different kinds of pants are
6 × 8 × 6 × 4 = 1152 in number.

Self Assessment

Fill in the blank:
1. .......................... is the method of arrangement of things.

2. A permutation is defined as an .......................... of a group of objects in a specific order.

12.2 Factorial

Factorials are just products, specified by an exclamation mark. For example, “four factorial” is
stated as “4!” and means 1 × 2 × 3 × 4 = 24. Generally, n! means the product of all the whole
numbers from 1 to n; that is, n! = 1 × 2 × 3 ×... × n.
Factorial identifies the number of different ORDERS in which one can assemble or place set of
items
n!= n × (n–1) × (n–2) × (n–3)...3 × 2 × 1
A factorial symbolizes the multiplication of consecutive natural numbers.

Did u know? For many reasons, 0! is defined to be equal to 1, not 0. Remember 0! = 1.

Example: Evaluate 6!.
1 × 2 × 3 × 4 × 5 × 6 = 720
Simplify 12!

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