Question

you are trying to form a 6-letter code from the 26 letters of the alphabet. suppose your code must follow the following rules:

* the first two letters must be different vowels ( AEIOU). ( this means no repeats.)

* the next two letters have no restrictions in other words, any letter is fine.)

* the last two letters cannot be a vowel, but they could repeat.

how many different codes are possible?

Answer 1

he first alphabets need to vowels without repetition

There are 5 vowels.

The first alphabet can be selected from 5 vowels.
The second alphabet can be selected from 4 vowels. (Since one have been used in the first alphabet of the code)

Next two letters can be filled with any alphabet.
hence both the letters can choose from 26 alphabets.

The last two cannot be vowels. We have 21 non-vowel alphabet hence we they can be selected from 21 alphabets.

Hence to summarize this we have

Hence the number of possible combinations = (5)*(4)*(26)*(26)*(21)*(21) = 5962320