The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is _______.
Answer (integer)
2454
Solution
2A, 2I, 2N, E, X, M, T, O
<br><br>To form four letter words
<br><br><b>Case 1 :</b> All same ( not possible)
<br><br><b>Case 2 :</b> 1 different, 3 same (not possible)
<br><br><b>Case 3 :</b> 2 different, 2 same
<br><br>= <sup>3</sup>C<sub>1</sub> $\times$ <sup>7</sup>C<sub>2</sub> $\times$ ${{4!} \over {2!}}$ = 756
<br><br><b>Case 4 :</b> 2 same of one kind, 2 same same of other kind
<br><br>= <sup>3</sup>C<sub>2</sub> $\times$ ${{4!} \over {2!2!}}$ = 18
<br><br><b>Case 5 :</b> All letters are different
<br><br>= <sup>8</sup>C<sub>4</sub> $\times$ 4! = 1680
<br><br>$\therefore$ Total ways = 1680 + 756 + 18 = 2454
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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