Question

how many words can be formed with the letter EQUATION which start with a vowel and ends with a vowel​

Answer 1

       

I'm not sure that my answer is right. Hope this helps.

Here, the first and last letters should be vowels. So, taking the two ends as V and the others as X, the words should in the form,

VXXXXXXV

The word EQUATION is an 8 letter word and contains no letter repetition.

There are all 5 vowels in the word EQUATION.

A, E, I, O, U.

At the two ends of the word which are indicated as V, these 5 vowels can be arranged in 5P2 = 5! / 3! = 20 ways.

In each 20 ways, the other 6 letters, which are to be placed at X, are arranged in 6P6 = 6! = 720 ways.

E.g.: Let E be at left and U be at right. So the other letters Q, A, T, I, O and N are placed in between E and U in 720 ways.

The same is occurred in other 19 arrangements of vowels at ends, even when E at right and U at left.

So the answer would be 5P2 × 6P6 = 20 × 720 = 14400.

Hope this helps.

If this is right and helps you, please mark it as the brainliest.

Thank you. :-))