how many different seven letter arrangements can be made from the letters in the word ability
The word "ability" has 7 letters.
To find the number of different arrangements, we need to use the permutation formula:
P(n, r) = n! / (n - r)!
where n is the total number of items and r is the number of items being arranged.
In this case, n = 7 (because there are 7 letters in the word "ability") and r = 7 (because we are arranging all 7 letters).
Therefore, the number of different seven-letter arrangements that can be made from the letters in the word "ability" is:
P(7, 7) = 7! / (7 - 7)! = 7! / 0! = 7! / 1 = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
So, there are 5040 different seven-letter arrangements that can be made from the letters in the word "ability".
To find the number of different seven-letter arrangements that can be made from the letters in the word "ability," you can use the concept of permutations.
The word "ability" has 7 letters, but it contains repeated letters (such as 'i' and 'b'). To calculate the number of arrangements, we need to take these repetitions into account.
1. Calculate the total number of letters (n) in the word: n = 7.
2. Count the number of times each different letter appears in the word:
- Letter 'a' appears once.
- Letter 'b' appears once.
- Letter 'i' appears twice.
- Letter 'l' appears once.
- Letter 't' appears once.
- Letter 'y' appears once.
3. Calculate the factorial of the total number of letters in the word (n!): 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
4. Adjust for the repeated letters by dividing the factorial by the factorial of each repeated letter. In this case, we divide by the factorial of 2 (because 'i' appears twice): 5040 / 2! = 5040 / (2 x 1) = 2520.
Therefore, there are 2520 different seven-letter arrangements that can be made from the letters in the word "ability."