# SOLUTION: How many four letter words can be made using the letters of the word 'MATHEMATICS'?

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Permutations Question 4492: How many four letter words can be made using the letters of the word 'MATHEMATICS'?Answer by khwang(438)   (Show Source): You can put this solution on YOUR website! Sol: Total 11 letters: 2 M, 2A, 2T,1 E, 1 I,1 C,1 H,1 S( three doubles, 5 singles) i) The word containing only 2 letters, as XXYY: C(3,2) 4!/2*2 = 3*6. ii) The word containing only 3 letters as XXYZ: C(3,1)C(7,2) 4!/2 = 3*21*12 iii) The word containing only 4 letters as XXYZ as XYZW: C(8,4) 4! = 8*7*6*5. then add up the results of the above 3 cases together to get the final answer.