Question

letters of the word equation is arranged in a row. find the probability that the arrangement starts with a vowel and ends with a consonant.

Answer 1

The word "equation" has 5 vowels and 3 consonants.
The number of arrangements starting with a vowel and ending with a consonant can be found as follows:
There are 5 choices for the first letter. The next 6 letters must consist of 4 vowels and 2 consonants, giving 6! * 3 arrangements, the reason for the 3 multiplier being that there are 3 combinations of the 3 consonants taken 2 at a time. This leaves a consonant to be the end letter. Therefore the number of arrangements starting with a vowel and ending with a consonant is given by:
\[\large 5\times6!\times3\]
The total number of arrangements of the 8 letters in "equation" is 8!
So the probability that the arrangement starts with a vowel and ends with a consonant is given by:
\[\large \frac{5\times6!\times3}{8!}=you\ can\ calculate\]

Answer 2

@kropot72 thank you :)

Answer 3

You're welcome :)