# How many words of 7 letters can be created that start with a vowel and end with the letter Q? Note that a word is any combination of 7 capital letters and letters can be repeated.

How many words of 7 letters can be created that start with a vowel and end with the letter Q? Note that a word is any combination of 7 capital letters and letters can be repeated.

We can solve this problem by finding how many ways to fill each letter of 7 letters and then multiply(using multiplication rule) them together.

There are 7 letters. First letter could be filled with any of the 5 vowels.

So, first letter could be filled in 5 ways.

The repetition is allowed. So, second letter can be filled with 7 ways.

Third letter can be filled with again 7 ways because repetition is allowed.

Fourth letter is filled with again any of the 7 letters.

Fifth letter is filled with again any of the 7 letters.

Sixth letter is filled with again any of the 7 letters.

Seventh letter is filled with 1 way, because we need to fill it with ‘Q’.

So, the number of possible ways = 5*7*7*7*7*7*1 =84035 ways.