4 letters are typed, without repetition. What is the probability that all 4 will be vowels? Write your answer as a percent. Round your answer to three decimal places

0,026%

Step-by-step explanation:

We have 26 letters in the alphabet and 5 of them are vowels.

When typing the first letter, we need it to be a vowel. As there are 5 vowels, the probability of one of them being typed is 5/26 (we have 5 right options in a total of 26).

Now, when typing the 2nd letter, we will assume that we already had typed a vowel because that's what we need. So now we have 4 options to be typed because we can't repeat the vowel. The probability of getting a vowel on the 2nd place is 4/26.

On the 3rd place we will have 3 vowels available and the probability of typing another vowel is 3/26.

On the 4th place we will have 2 vowels available and the probability of typing another vowel is 2/26.

As we need this to happen all at the same time, we need to multiply all the probabilities. That is

5/26 * 4/26 * 3/26 * 2/26 = 0,026%

Therefore, the probability of the 4 will be vowels is 0,026%.