The letters LACSIPE fell off a billboard. How many different ways can the letters be arranged,
hoping to find the correct spelling of SPECIAL?
There are 7 different letters.
These can be arranged in 7! ways or 5040 ways.
Ah, the case of the missing letters! Quite a puzzling situation indeed. Let's see if we can arrange those jumbled letters to spell out "SPECIAL".
Now, since the letters have fallen off the billboard and we don't want any "SPLEICA" mishaps, let's figure out the number of ways we can arrange them correctly.
The word "SPECIAL" has 7 letters, so we need to arrange those 7 letters in a specific order.
Using a little math magic, we can calculate the number of permutations by taking the factorial of the number of letters.
So, let's do some quick calculations:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
Voila! There are 5040 different ways the letters can be arranged to form the word "SPECIAL". Just make sure you don't accidentally spell out "PLACISE" or "CLEAPIS" along the way!
To find out how many different ways the letters can be arranged to spell SPECIAL, we can use the concept of permutations.
We have 7 letters: L, A, C, S, I, P, E.
The word we want to form is SPECIAL, which consists of 7 letters.
Using the formula for permutations, which is nPr = n!/(n-r)!, where n is the total number of items and r is the number of items taken at a time, we can calculate the number of arrangements.
In this case, we have 7 letters, so n = 7.
Since we want to find all possible arrangements, r will also be 7.
Plugging these values into the formula:
7P7 = 7!/(7-7)! = 7!/0! = 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
Therefore, there are 5040 different ways the letters LACSIPE can be rearranged to spell SPECIAL.
To find the number of different ways the letters can be arranged to form the correct spelling of "SPECIAL," we need to determine the number of permutations.
First, let's identify the number of occurrences for each letter in the word "SPECIAL" and the given set of letters "LACSIPE."
In "SPECIAL," we have:
- S appears once
- P appears once
- E appears twice
- C appears once
- I appears once
- A appears once
- L does not appear in "SPECIAL."
From the given set of letters "LACSIPE," we have:
- L appears once
- A appears once
- C appears once
- S appears once
- I appears once
- P appears once
- E appears once
We need to find the number of permutations by considering these occurrences.
The formula to calculate the number of permutations is: n! / (n1! * n2! * n3! * ... * nk!)
Where:
- n is the total number of objects (total number of letters)
- n1, n2, ..., nk are the occurrences of each letter
Using this formula, we can calculate the number of permutations for "SPECIAL" using the given set of letters "LACSIPE."
n = total number of letters = 8 (since there are 8 letters in "SPECIAL")
n1 = occurrence of S = 1
n2 = occurrence of P = 1
n3 = occurrence of E = 2
n4 = occurrence of C = 1
n5 = occurrence of I = 1
n6 = occurrence of A = 1
Using the formula, we get:
8! / (1! * 1! * 2! * 1! * 1! * 1!) = 40,320 / (1 * 1 * 2 * 1 * 1 * 1) = 40,320
Therefore, there are 40,320 different ways to arrange the letters "LACSIPE" in order to spell "SPECIAL" correctly.