Find the number of words which can be formed by using the letters of the word EQUATION if each word has to start with a vowel.
I'll be glad to add to your list if I can.
25200
To find the number of words that can be formed by using the letters of the word "EQUATION" if each word has to start with a vowel, we need to consider the arrangement of the remaining letters.
Let's break down the word "EQUATION" into its constituent letters: E, Q, U, A, T, I, O, and N.
Since we need each word to start with a vowel, we ignore the consonants Q, T, and N and focus on the vowels E, U, A, I, and O.
We have 5 vowels to choose from for the first position of the word. Once we select one of these vowels, we are left with the remaining 6 letters to arrange for the rest of the word (Q, U, E, A, T, and I). The remaining letters can be arranged in 6! (factorial) ways.
To calculate the total number of words, we multiply the number of ways to choose the vowel for the first position and the number of ways to arrange the remaining letters:
Number of words = Number of ways to choose the first vowel * Number of ways to arrange the remaining letters
= 5 * 6!
Therefore, the number of words that can be formed by using the letters of the word "EQUATION" if each word has to start with a vowel is 5 * 6! (factorial).