How many distinct permutations of the letters of the word OTTAWA being and end with the letter T?
I did 6!/2! :S but i get 360.
I tried 6P2=30
I am getting it wrong...
help please.
It is 4P2=12
or
4!/2!
=24/2
=12
To find the number of distinct permutations of the letters of the word OTTAWA that end with the letter T, you need to consider the placement of the other 5 letters (excluding T).
Let's break it down step-by-step:
1. Identify the given word: OTTAWA.
2. Count the total number of letters in the word: 6.
3. Identify the letter that needs to be at the end: T.
4. Determine the number of available positions for the other letters: 5 (excluding T).
5. Calculate the number of ways to arrange the remaining 5 letters in the available positions using the formula for permutations: 5P5 = 5!.
6. Simplify the calculation: 5! = 5 x 4 x 3 x 2 x 1 = 120.
7. Therefore, there are 120 distinct permutations of the letters of the word OTTAWA that end with the letter T.
So, the correct result is 120, not 360 or 30.
To find the number of distinct permutations of the letters in the word "OTTAWA" that end with the letter "T," you need to consider the distinct arrangements for the other five letters before "T."
First, let's calculate the total number of distinct permutations of the letters in the word "OTTAWA."
The word "OTTAWA" has six letters, so we have a total of 6! (6 factorial) arrangements.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
However, this count includes arrangements where the letter "T" is not at the end.
To find the number of permutations that end with the letter "T," we need to consider the remaining five letters, which are "O," "T," "T," "A," and "W."
The two "T's" are indistinguishable, so we need to account for that when counting the distinct permutations.
Since there are two "T's," we divide the total number of permutations by 2! (2 factorial) to eliminate the repeated arrangements.
2! = 2 x 1 = 2
Now, we can calculate the number of distinct permutations that end with the letter "T":
Distinct permutations = (Total permutations)/(Repeated arrangements)
Distinct permutations = 720/2 = 360
Therefore, there are 360 distinct permutations of the letters in the word "OTTAWA" that end with the letter "T."