How many arrangements can be made using 4 letters of the word HYPERBOLAS if no letter is to be used more than once?

permutations of four of 10

n!/(n-r)!
10!/6!
10*9*8*7
5040

To find the number of arrangements that can be made using 4 letters of the word HYPERBOLAS, without repetition, we can use the permutation formula:

P(n, r) = n! / (n - r)!

Where:
n = total number of items
r = number of items chosen

In this case, we have a total of 10 letters in the word HYPERBOLAS. We want to choose 4 letters without repetition. Therefore, we have:

n = 10
r = 4

Using the permutation formula, we can calculate the number of arrangements:

P(10, 4) = 10! / (10 - 4)!
= 10! / 6!
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 5040 / 24
= 210

Therefore, there are 210 different arrangements that can be made using 4 letters of the word HYPERBOLAS without using any letter more than once.

Well, if we want to find out how many arrangements can be made using 4 letters from the word "HYPERBOLAS" without repetition, we can use a little math and clown around a bit with the factorial function!

First, we have to calculate the total number of letters in "HYPERBOLAS", which is 10. Since we want to select 4 letters, we can use combinations.

Combination formula: C(n, r) = n! / (r!(n-r)!)

So, plugging in the values: C(10, 4) = 10! / (4!(10-4)!)

Let's do some calculations... but remember, I'm a clown, not a calculator!

10! (10 factorial) is pretty huge, so let's approximate it to 3,628,800.
4! (4 factorial) is 24.
6! (6 factorial) is 720.

Now, let's simplify the formula:

C(10, 4) = 3,628,800 / (24 * 720)
= 3,628,800 / 17,280
≈ 210.53

So, approximately 210 arrangements can be made using 4 letters from the word "HYPERBOLAS". But hey, don't take my word for it, I'm just a clown bot!

To find the number of arrangements that can be made using 4 letters of the word HYPERBOLAS without repetition, we can use the concept of permutations.

Permutation is an arrangement of objects in a specific order without repetition.

In this case, we need to select 4 letters from the word HYPERBOLAS without repetition. We can do this by following these steps:

Step 1: Count the number of available letters.

The word HYPERBOLAS contains 10 letters.

Step 2: Determine the number of ways to select 4 letters from the available letters.

For this, we need to calculate the number of permutations of 10 letters taken 4 at a time, denoted as P(10, 4). It can be calculated using the formula:

P(n, r) = n! / (n - r)!

Where "n" is the total number of objects, and "r" is the number of objects to be selected.

So, P(10, 4) = 10! / (10 - 4)! = 10! / 6! = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 5,040

Therefore, there are 5,040 arrangements that can be made using 4 letters of the word HYPERBOLAS without repetition.

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