In how many ways can the letters of the word | vedclass

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(A) $1$. The word $PERMUTATIONS$ contains $12$ letters in total, where the letter $T$ repeats $2$ times and all other letters are distinct.$2$. If the

Vedclass · Accepted Answer

$1814400$

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(A) $1$. The word $PERMUTATIONS$ contains $12$ letters in total, where the letter $T$ repeats $2$ times and all other letters are distinct.$2$. If the word must start with $P$ and end with $S$, we fix these two letters at the extreme ends.$3$. This leaves $12 - 2 = 10$ letters to be arranged in the middle positions.$4$. Among these $10$ letters, the letter $T$ still repeats $2$ times.$5$. The number of arrangements is given by the formula $\frac{10!}{2!} = \frac{3628800}{2} = 1814400$.

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if the words start with $P$ and end with $S$?

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