Question

How

many arrangements can be made out of the letters of the
word "PROUGHT", the vowels never being together?

Answer 1

The number of arrangements that can be made out of the letters of the word 'PROUGHT', with vowels never being together, is 14,400.

Step-by-step explanation:

To calculate the number of arrangements that can be made out of the letters of the word 'PROUGHT' without the vowels being together, we need to apply the principle of permutations. Consider the consonants 'PRGHT' as a single unit. This gives us 5 units ('PRGHT' and 'O') to arrange. Now, there are 5! ways to arrange these 5 units. However, within the 'PRGHT' unit, the letters can be arranged in 5! ways as well. Therefore, the total number of arrangements is 5! * 5!. Let's calculate:

1. Arrange the 'PRGHT' unit: 5! = 120
2. Arrange the vowels and the 'O' unit: 5! = 120

Now, multiply these two values together to get the total number of arrangements without the vowels being together: 120 * 120 = 14,400.

Learn more about Calculating the number of arrangements with a restriction