Question

How many 3 letter words can be formed from the letters of the word calcutta?

Answer 1

Given: The word CALCUTTA

To find: 3 letter words that can be formed from above word.

Solution:

• Now in order to form three letters, lets consider some cases.

• Case 1: All the letters are unique

• So there are 5 different letters that is C, A, L, U and T

• Now taking 3 letters at a time, arrangements possible are:

            5P3 = 5! / (5-3)!

                   = 5 x 4 x 3

                   = 60

• Case 2: Two letters are same  and one is different.

• The 2 repeating letters are C, A and T - 3 choices

• 3rd letter can be any letter of remaining 4 letters  - 4 choices

• Arrangement of 3 letters will be: 3!

• But we will divide the total by 2! to avoid extra counting because of the 2 repeating letters.

• Therefore, total  

                =  3  x  4  x  3!  / 2!

                = 36

• Case 3:  All the letters are same

• In this case  no such arrangements possible. because none of the letter is occurring thrice.

• So the total ways are:

               60 + 36

              = 96

Answer:

               So the total ways are 96.