Sum

Determine the number of arrangements of letters of the word ALGORITHM if O is the first and T is the last letter.

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#### Solution

A word is to be formed using the letters of the word ALGORITHM.

There are 9 letters in the word ALGORITHM.**When beginning with O and ends with T:**

All the letters of the word ALGORITHM are to be arranged among themselves such that arrangement begins with O and ends with T.

7 letters other than O and T can be filled between O and T in ^{7}P_{7} i.e., 7! ways = 5040 ways.

∴ 5040 words beginning with O and ending with T can be formed.

Concept: Concept of Permutations - Permutations When Repetitions Are Allowed

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