how many different seven letter arrangements can be made from the letters in the word ability

1 answer

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".