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Question

find the number of ways in which 4 different letters of the word MATHEMATICS can be arranged.

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Solution

Word MATHEMATICS has 11 words, three from 11 words are repeating.
M, A and T are repeating more than one times.
Observe that, there are 8 choices for the first word
Number of choices for the second word = 7
Number of choices for the third word = 6
Number of choices for the fourth word = 5
Therefore, total number of choices = 8 × 7 × 6 × 5 = 1680

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