Question

How many strings of eight english letters are there that start with a vowel, if letters cannot be repeated?

Answer 1

We know there are 5 vowels

To make a string of 8 letters the first letter should be a vowel only that means there are 5 choices for first position .

one vowel out of 5 can be chosen in total 5 ways .

Next 7 letters can be chosen out of any 4 vowels and 21 consonants.

there are total 25 choices available and we have to pick any 7

there would be 25P 7 ways to choose them . here P stand for permutation.

so total number of strings we can made are 5* (25 p7) = 5 * 2422728000

Answer : =12113640000