# What are the number of different words beginning and ending with a consonant, which can made out of the word "EQUATION" ? (Using the concept of Permutations-Combinations)

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The word "Equation" has 8 letters all of which are unique.

We want the number of letter arrangements that start and end with a consonant. Let's first see that with letter arrangements, we're working with permutations (we care about the order of things). The general formula is:

First let's work with the end letters. We only want consonants (there are 3 of them), which gives:

In total then, we have

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There are 120 different words beginning and ending with a consonant that can be made out of the word "EQUATION".

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