NCERT Book Class 11 Maths Chapter 6 Permutations and Combinations

100 MATHEMATICS

Chapter 6
PERMUTATIONS AND COMBINATIONS

vEvery body of discovery is mathematical in form because there is no
other guidance we can have – DARWINv

6.1 Introduction
Suppose you have a suitcase with a number lock. The number
lock has 4 wheels each labelled with 10 digits from 0 to 9.
The lock can be opened if 4 specific digits are arranged in a
particular sequence with no repetition. Some how, you have
forgotten this specific sequence of digits. You remember only
the first digit which is 7. In order to open the lock, how
many sequences of 3-digits you may have to check with? To
answer this question, you may, immediately, start listing all
possible arrangements of 9 remaining digits taken 3 at a
time. But, this method will be tedious, because the number
Jacob Bernoulli
of possible sequences may be large. Here, in this Chapter, (1654-1705)
we shall learn some basic counting techniques which will
enable us to answer this question without actually listing 3-digit arrangements. In fact,
these techniques will be useful in determining the number of different ways of arranging
and selecting objects without actually listing them. As a first step, we shall examine a
principle which is most fundamental to the learning of these techniques.

6.2 Fundamental Principle of Counting
Let us consider the following problem. Mohan has 3 pants and 2 shirts. How many
different pairs of a pant and a shirt, can he dress up with? There are 3 ways in which
a pant can be chosen, because there are 3 pants available. Similarly, a shirt can be
chosen in 2 ways. For every choice of a pant, there are 2 choices of a shirt. Therefore,
there are 3 × 2 = 6 pairs of a pant and a shirt.