Dear Rachita,

Basic Principles of Counting

Illustration:

How many 4-letter words can be formed using a, b, c, d, e

        (i) Without repetition                (ii) With repetition

Solution:

(i) The number of words that can be formed is equal to the number of ways to fill the three places.

                  Places:                                  

       Number of Choices:                        5        4        3           2

        => 5 × 4 × 3 × = 120 words can be formed when repetition is not allowed.

(ii) The number of words that can be formed is equal to the number of was to fill the three places.

              Places:                                 

     Number of Choices:                      5        5        5         5

First place can be filled in 5 ways. If repetition is allowed, all the remaining places can be filled in 5 ways each.

        => 5 × 5 × 5 × 5 = 625 words can be formed when repetition is allowed.

Exercise

1. 1 Plane, 2 trains and 3 buses ply between Delhi and Agra.

        (a) In how many ways can you to Agra from Delhi.

        (b) In how many ways can you go and come back if you go by train,

2. Total number of combinations of n dissimilar things, taken at least one at a time ________.

Ans.1 (a) 6,

         (b) 2 × = 12

2. 2ⁿ - 1

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Aman Bansal

Askiitian Expert

identical letters cannot permute among themselves

therefore, 6!/2!x2!