Use the formula for to solve.
How many arrangements can be made using 3 letters of the word HYPERBOLAS if no letter is to be used more than once?
10P3 = 10*9*8
Well, let's not go overboard with hyperboLAStic estimates here. To solve this problem, we'll use a simple formula called the "permutation formula." It goes like this:
The number of ways to arrange n objects taken r at a time is given by n!/(n-r)!
So, in this case, we have 9 letters in the word HYPERBOLAS, and we want to arrange 3 of them.
Using the permutation formula, we get:
9! / (9-3)!
Calculating this, we get:
9! / 6!
Now let's see if humor can rearrange our thinking here...
HYPERBOLAS, hey? That's a pretty intense word, like a really complicated yoga pose. I don't know if I can stretch my funny bone to come up with a specific number for you, but I can promise you this: there are definitely more than 3 ways to arrange those letters! In fact, there are quite a few. So feel free to let your imagination run wild and create as many HYPERBOLAS arrangements as it takes to make you happy!
To solve this problem, we can use the formula for permutations, which is given by:
P(n, r) = n! / (n - r)!
where n is the total number of items to choose from, and r is the number of items to choose.
In this case, we want to find the number of arrangements of 3 letters from the word HYPERBOLAS, without repeating any letters. So, we can substitute n = 10 (the total number of letters in HYPERBOLAS) and r = 3 into the formula:
P(10, 3) = 10! / (10 - 3)!
= 10! / 7!
Now, let's calculate:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Substituting these values into the formula:
P(10, 3) = 3,628,800 / 5,040
≈ 720
Therefore, there are approximately 720 different arrangements that can be made using 3 letters from the word HYPERBOLAS without repeating any letters.
To solve this problem, we can use the formula for permutations, which is given by:
nPr = n! / (n - r)!
Where "n" represents the total number of items, and "r" represents the number of items you want to use in each arrangement.
In this problem, we want to find the arrangements of 3 letters from the word HYPERBOLAS, without repeating any letter. So, in this case, "n" would be the total number of distinct letters in the word, and "r" would be the number of letters in each arrangement (which is 3 in this case).
Let's calculate it step by step:
Step 1: Calculate the factorial of the total number of distinct letters:
n! = 10!
Step 2: Calculate the factorial of the difference between the total number of distinct letters and the number of letters in each arrangement:
(n - r)! = (10 - 3)!
Step 3: Divide the two factorials:
nPr = 10! / (10 - 3)!
Now, we can calculate the value:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
(10 - 3)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
Finally, we can substitute these values into the formula:
nPr = 3,628,800 / 5,040
Therefore, the number of arrangements that can be made using 3 letters from the word HYPERBOLAS, without repeating any letter, is equal to 720 arrangements.