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How many words can be formed from all the letters of the word 'INITIAL' such that all words must have started and ended with letter 'I'?

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closed as off-topic by Namaste, Gregory Grant, Yujie Zha, Shailesh, Leucippus Jul 24 '17 at 0:56

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Just fix two $I's$ in front and last $$\{I,\_,\_,\_,\_,\_,I\}$$

Now you have five objects

$$\{N,I,T,A,L\}$$

And their permutation is $$5!=120$$

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'INITIAL' has 7 letters. You know that 2 of them have to stay at the beginning and at the end of the word, so 2 (I) letters and 2 (start and end) position are "blocked".

You need to think to the middle positions. Middle positions are 5 and you have 5 letters. So, you want all the words can be formed by the positions of the letters: you need to use disposition of 5 objects in 5 positions: PERMUTATION.

$$ D_{5,5}= P_5=5! $$

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