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.

(5 C 4 * 21 C 0)/26 C 4= 3.344481605E-4 = 0.0003344481605

*100= 0.03344481605% = 0.033%

C: Combinations on Ti-84 Plus Calculator

Hope this helps =D

Well, let's think about this. There are five vowels in the English language - A, E, I, O, U. And we need to pick 4 letters without repetition.

So the total number of ways to pick 4 letters out of 26 (the number of letters in the English alphabet) without repetition is 26 choose 4, which is equal to 26! / (4!(26-4)!) = 26! / (4!22!) = (26 * 25 * 24 * 23) / (4 * 3 * 2 * 1) = 65,780.

Now, since we are looking for all 4 letters to be vowels, there are only 5 vowels to choose from. So the total number of ways to pick 4 vowels out of 5 without repetition is 5 choose 4, which is equal to 5! / (4!(5-4)!) = 5! / (4!1!) = 5.

Therefore, the probability of all 4 letters being vowels is 5/65,780 = 0.000076 or 0.008%.

So, the answer is 0.008%. Keep in mind, though, that this is just the probability and doesn't guarantee that the letters will actually be vowels. Like the saying goes, sometimes life just doesn't give you the vowels you want!

To find the probability of all 4 letters being vowels, we need to know the number of vowels and the total number of possible outcomes.

There are 5 vowels in the English alphabet: A, E, I, O, and U.

Since there are no repeating letters allowed, the total number of possible outcomes is obtained by considering the available options for each position. For the first position, there are 5 choices (any vowel), for the second position, there are 4 choices remaining (since no repetition is allowed), for the third position, there are 3 choices remaining, and for the fourth position, there are 2 choices remaining.

Therefore, the total number of possible outcomes is 5 * 4 * 3 * 2 = 120.

The number of favorable outcomes (all 4 letters being vowels) is 5 * 4 * 3 * 2 = 120 (since there are 5 vowels to choose from for each position).

Now, we can calculate the probability as the number of favorable outcomes divided by the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes
= 120 / 120
= 1

Finally, we convert the probability to a percentage by multiplying by 100:

Probability (as a percent) = 1 * 100
= 100

Therefore, the probability of all 4 letters being vowels is 100%.

To find the probability that all 4 letters will be vowels, we need to determine the number of ways we can select 4 vowels from the set of vowels (A, E, I, O, U) and divide it by the total number of ways we can select 4 letters without repetition from the 26 English alphabets.

The set of vowels consists of 5 elements (A, E, I, O, U).

The total number of ways we can select 4 letters without repetition from the 26 English alphabets is given by "26 choose 4" (denoted as C(26, 4)).

The formula for "n choose k" is given by n! / (k! * (n - k)!)

Therefore, "26 choose 4" can be calculated as follows:

C(26, 4) = 26! / (4! * (26 - 4)!)
= (26 * 25 * 24 * 23) / (4 * 3 * 2 * 1)
= 14,950

Now, we need to determine the number of ways we can select 4 vowels from the set of vowels (A, E, I, O, U). This can be calculated as "5 choose 4".

C(5, 4) = 5! / (4! * (5 - 4)!)
= (5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1)
= 5

Finally, we can calculate the probability by dividing the number of ways to select 4 vowels by the total number of ways to select 4 letters:

Probability = (Number of ways to select 4 vowels) / (Number of ways to select 4 letters)
= 5 / 14,950
≈ 0.000334

To express this as a percentage, we can multiply the probability by 100:

Percentage probability = Probability * 100
≈ 0.0334%

Therefore, the probability that all 4 letters typed will be vowels is approximately 0.0334%.

Assuming you count 5 vowels, and no repetition ,

prob(4 vowels in 4 tries)
= (5/26)(4/25)(3/24)(2/23) = .....