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Question

How many different words can be formed by taking four letters at a time from the letters of the word "MATHEMATICS" ?
  1. 2454
  2. 4908
  3. 3246
  4. 5216


Solution

The correct option is A 2454
Here M,A, and T occur twice, rest all words one time.
Three cases possible:-
CASE 1-All the words are different
               8C4 ×4!
CASE 2:-Two same and two different
                3C1×7C2×4!2!
CASE 3:-Two same of 1st kind and two
                same of 2nd kind 
3C2×4!2!×2!
Answer is (CASE 1+CASE 2+CASE 3) =2454 

 

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