Question

The letters of the word EQUATION are arranged in a row. Find the
probability that the arrangement starts with a vowel and ends with a consonant.

Answer 1

Let's start with the vowels first: There are 5 choices for the first letter of the resulting word.
Let's move on to the last letter that must be a consonant: There are 3 choices for the last letter of the word.(Q,T,N)
Now, out of the total 8 letters, we have already decided first and the last letters so the choices for the rest of the letters will be:(assuming no letters are repeated)
1st:5(A,E,I,O,U)
2nd: 6
3rd: 5
4th: 4
5th: 3
6th: 2
7th: 1
8th:3(Q,T,N)
So the total number of combinations will be: (5)x6x5x4x3x2x1x(3)=10800

Now, total number of combinations of any 8 letter word formed out of letters of the word 'EQUATION' will be 8!= 40320.

Therefore probability= 10800/40320=0.2678571429.