Question
How nay ways can the letters in the word EDUCATION be arranged?
A.
1
B.
9
C.
40,320
D.
362,880
A.
1
B.
9
C.
40,320
D.
362,880
Answers
GPT-4o mini
To determine the number of ways to arrange the letters in the word "EDUCATION," we first need to find out how many letters it has and if there are any repeated letters.
The word "EDUCATION" consists of 10 letters: E, D, U, C, A, T, I, O, N.
We can notice that all the letters are unique (no repetitions). To find the number of arrangements of these letters, we can use the factorial of the number of letters:
Number of arrangements = \(10!\)
Calculating \(10!\):
\[
10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800
\]
However, the options given in the question do not include 3,628,800. Let’s explore the options again:
- A. 1
- B. 9
- C. 40,320
- D. 362,880
After analyzing, we can see that none of the provided choices match our computed result. But if we consider the total arrangements for the word "EDUCATION" as suggested, it is fundamentally confirmed to be \(3,628,800\).
If the closest answer based on standard factorial results is sought, while also considering \(9!\), it equals \(362,880\) which appears in option D.
Thus, the correct answer from the given choices, acknowledging any discrepancies, would be:
**D. 362,880**
This would be the correct conclusion to follow within the listed options, presuming an error in initial computation of the total arrangements.
The word "EDUCATION" consists of 10 letters: E, D, U, C, A, T, I, O, N.
We can notice that all the letters are unique (no repetitions). To find the number of arrangements of these letters, we can use the factorial of the number of letters:
Number of arrangements = \(10!\)
Calculating \(10!\):
\[
10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800
\]
However, the options given in the question do not include 3,628,800. Let’s explore the options again:
- A. 1
- B. 9
- C. 40,320
- D. 362,880
After analyzing, we can see that none of the provided choices match our computed result. But if we consider the total arrangements for the word "EDUCATION" as suggested, it is fundamentally confirmed to be \(3,628,800\).
If the closest answer based on standard factorial results is sought, while also considering \(9!\), it equals \(362,880\) which appears in option D.
Thus, the correct answer from the given choices, acknowledging any discrepancies, would be:
**D. 362,880**
This would be the correct conclusion to follow within the listed options, presuming an error in initial computation of the total arrangements.