Permutations And Combinations Question 281

Question: How many words can be formed with the letters of the word MATHEMATICS by rearranging them [MP PET 1984; DCE 2001]

Options:

A) $ \frac{11\ !}{2\ !\ 2\ !} $

B) $ \frac{11\ !}{2\ !} $

C) $ \frac{11\ !}{2\ !\ 2\ !\ 2\ !} $

D) $ 11\ ! $

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Answer:

Correct Answer: C

Solution:

  • Since there are 2 M’s, 2 A’s and 2T’s.
    $ \therefore $ Required number of ways are $ \frac{11\ !}{2\ !\ 2\ !\ 2\ !} $ .