Find the number of arrangements of the letters of the word president
There are 9 letters in the word "president". To find the number of arrangements, we can use the formula for permutations:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects being selected.
In this case, we want to find the number of arrangements of all 9 letters, so we have:
9P9 = 9! / (9 - 9)! = 9! / 0! = 362,880
Therefore, there are 362,880 possible arrangements of the letters in the word "president".
To find the number of arrangements of the letters in the word "president," we can use the formula for permutations.
The word "president" has a total of 9 letters.
Now, let's look at the repetition of letters.
The letter "e" appears twice, and the letter "r" appears twice.
Therefore, we need to adjust the formula to account for these repetitions.
The formula for permutations with repetition is given by:
n! / (r1! * r2! * ... * rk!)
Where n is the total number of items and r1, r2, ..., rk are the repetitions of each item.
In this case, n = 9, r1 = 2 (for "e"), and r2 = 2 (for "r").
Using the formula, the number of arrangements is:
9! / (2! * 2!)
= (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((2 * 1) * (2 * 1))
= 362,880 / 4
= 90,720
Therefore, the number of arrangements of the letters in the word "president" is 90,720.