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  4. The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is:

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Q. The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with $T$ is:

Permutations and Combinations

Solution:

The word MATHEMATICS contains 11 letters viz. M, M, A, A T, T, H, E, I, C, S. The number of words that begin with $T$ and end with $T$ is
$\frac{9 !}{2 ! 2 !}=90720 $