Question

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)

Answer 1

4320 ways

Explanation:

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:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

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

`P_(3,2)=(3!)/(1!)=6`

For the letters in between the end letters, there are 6 of them (5 vowels and the one consonant we didn't use) and can be placed anywhere. That's `6! = 720`.

In total then, we have

`6xx720=4320`