How many arrangements are there of the letters in the word SEPTEMBER that start and end with the letter E?
there are 9 letters in all, and the two E's are taken.
That leaves 7 unique letters, so 7!
To find the number of arrangements of the letters in the word "SEPTEMBER" that start and end with the letter "E," we need to consider the remaining letters in the middle.
Step 1: Count the total number of arrangements of the letters in the word "SEPTEMBER."
The word "SEPTEMBER" has a total of 9 letters.
Step 2: Fix the position of the letter "E" at the beginning and end.
Since the word needs to start and end with the letter "E," we fix these positions. That leaves us with the remaining 7 letters: S, P, T, M, B, R.
Step 3: Count the number of arrangements of the remaining 7 letters.
There are 7 remaining letters, so the number of arrangements can be calculated as 7!.
Step 4: Multiply the number of arrangements from Step 3 by 2.
Since the letter "E" is fixed at both the beginning and end, we need to multiply the number of arrangements from Step 3 by 2.
Therefore, the total number of arrangements of the letters in the word "SEPTEMBER" that start and end with the letter "E" is:
2 * 7! = 2 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 2 * 5040 = 10080 arrangements.
To find the number of arrangements of the letters in the word "SEPTEMBER" that start and end with the letter E, we can follow these steps:
1. Count the number of times the letter 'E' appears in the word. In this case, it appears twice.
2. Treat the two 'E's as a single entity. Now, we have the letters 'S', 'P', 'T', 'M', 'B', and the group 'EE'.
3. Find the number of ways to arrange these six entities. The formula to calculate the number of arrangements of items with repetitions is given by n!/m!, where n is the total number of items and m is the number of repetitions.
In this case, we have n = 6 items to arrange (S, P, T, M, B, EE) and m = 2 repeated items (EE).
So, the number of arrangements is 6! / 2! = (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1) = 6 * 5 * 4 * 3 = 360.
Therefore, there are 360 arrangements of the letters in the word "SEPTEMBER" that start and end with the letter E.