Permutations and combinations
Fundamental principle of counting
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 x 2=6 pairs of a pant and a shirt.
A boy wants to buy 3 different books from a book shop. In that shop there are 5 different books. He selects 3 books out of 5. Selection of 3 books out of 5 is a combination. He arranges these books in his shelf in different ways every day. Each way of the arrangement of books is a permutation.
Definition: A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.
1. There are three boys: ASHRITH (A), BHARATH (B), and CHETAN(C). Arrange them in a row, two at a time. The arrangements are
There are 6 different ways of arrangements. These arrangements are called permutations.
Example 2: there are four different digits 2, 3, 4, 5. How many numbers can be formed using two digits at a time?
From four different digits, twelve 2-digit numbers are formed.
From the above examples it is clear that for 1
There are three boys: ASHRITH (A), BHARATH (B), and CHETAN(C). From these boys how many groups of two boys can be selected?
The selections are AB, AC and BC. So, 3 groups can be selected.
Note: Here AB and BA; AC and CA; BC and CB are not different selections
In general the number of combinations of n things taken r at a time is denoted by nCr.
Observe the following:
For 0 ≤ r ≤ n
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