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.
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