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.

this a permutation question ans, choose are
40320
1260
1080
400
25200

Examine the word to confirm:

1. that there are 8 distinct letters
2. that there are 5 vowels.

We note that:
a. We need to start the word with one of 5 vowels.
b. the remaining 7 letters can make 7!=5040 words.
=>
There is a total of 5*7!=25200 words.

5*7 =25200

Well, I guess I could come up with a "punny" response for each option, but that might just "permutation" me to a "perplexing" level.

Anyway, let's figure this one out. The word "EQUATION" has 8 letters, with 3 vowels (E, U, and A) and 5 consonants (Q, T, I, O, N).

We want to find the number of words that can be formed by using all the letters, but with the condition that each word starts with a vowel.

To solve this, we can start by fixing a vowel at the beginning and permuting the remaining letters.

There are 3 vowels to choose from, and after fixing one, we have 7 remaining letters to arrange. Therefore, there are 3 options for the first vowel and 7! (7 factorial) ways to arrange the remaining 7 letters.

Hence, the total number of words that can be formed is 3 * 7! = 3 * 5040 = 15120.

So, it looks like none of the given options match the correct answer. The correct answer is 15120.

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 can use permutation.

First, let's identify the vowels in the word "EQUATION," which are E, U, and A. Since each word has to start with a vowel, we need to fix the position of the first letter as one of these three vowels.

To solve this problem, we'll break it down into cases:
1. If the first letter is E: We have to arrange the remaining letters U, A, Q, T, I, O and N. So we have 7 letters to arrange, which can be done in 7! ways (7 factorial).
2. If the first letter is U: We have to arrange the remaining letters E, A, Q, T, I, O, and N. Again, we have 7 letters to arrange, which can be done in 7! ways.
3. If the first letter is A: We have to arrange the remaining letters E, U, Q, T, I, O, and N. Once more, we have 7 letters to arrange, which can be done in 7! ways.

Since the cases are mutually exclusive (we can't have more than one first letter), we need to sum up the number of arrangements in each case:

Total = Number of arrangements if first letter is E + Number of arrangements if first letter is U + Number of arrangements if first letter is A
Total = 7! + 7! + 7!

Calculating this, we get:
Total = 5040 + 5040 + 5040
Total = 15120

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 15,120.

My first time Cassandra rdd a Michelle gonzales.wich ones the answer.