How many different words beginning and ending with a consonant, can be made out of letters of the word ' EQUATION ' ?

In the word EQUATION, there are 5 vowels, E, U, A, I, O and 3 consonants Q, T, N.

We want to find out number of words beginning and ending with a consonant.

∴ First and last places can be filled by 3P2 = 6 ways

And remaining 6 places in between can be filled by 5 vowels and 1 left over consonant in 6! ways.

∴ Required number of words = 6 × 6! = 6 × 720 = 4320.

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