In how many ways can the letters of the word SOKOTO be permuted
There are 6 letters in the word SOKOTO.
To find the number of ways to permute them, we use the formula for permutations of n objects taken r at a time:
P(n,r) = n! / (n-r)!
In this case, we want to permute all 6 letters, so r = 6.
P(6,6) = 6! / (6-6)!
P(6,6) = 6! / 0!
P(6,6) = 6! / 1
P(6,6) = 720
Therefore, there are 720 ways to permute the letters of the word SOKOTO.
You have 6 letters, 3 of which are the same, so
number of permutations = 6!/3! = 120
The bot totally ignored the fact that we had 3 O's
and as a result got a totally wrong answer again.
I apologize for the mistake in my previous response. You are correct that there are 3 O's in the word SOKOTO, which means that we have to adjust the calculation accordingly to account for the repetition of these letters.
The correct formula to use in this case is the number of permutations of n objects taken r1, r2, ..., rk at a time, where r1, r2, ..., rk are the number of repetitions of each distinct object. This is given by:
P(n; r1, r2, ..., rk) = n! / (r1! r2! ... rk!)
Using this formula, we can find the number of permutations of the word SOKOTO as follows:
P(6; 2, 3, 1) = 6! / (2! 3! 1!)
P(6; 2, 3, 1) = (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1 x 3 x 2 x 1 x 1)
P(6; 2, 3, 1) = 720 / 12
P(6; 2, 3, 1) = 60
Therefore, there are 60 ways to permute the letters of the word SOKOTO.
Thank you for bringing the mistake to my attention, and I apologize for any confusion caused.
Geeesh!
NO!
Did you not read my correct answer ????
I apologize again for my mistake. I missed your correct answer when responding. You are correct that the number of permutations of the word SOKOTO, taking into account the repetitions of the letter O, is:
6!/3! = 720/6 = 120
Thank you for pointing out my mistake and providing the correct answer.
To find the number of ways the letters of the word SOKOTO can be permuted, we can use the concept of permutation.
The word SOKOTO has 6 letters, but it has repetition of letters - O (occuring twice).
To find the number of ways we can permute the letters, we can use the formula for permutation when there are repetitions.
The formula for permutation when there are repetitions is:
P(n; r_1, r_2, ..., r_k) = n!/(r_1! * r_2! * ... * r_k!)
where n is the total number of items, and r_1, r_2, ..., r_k are the repetitions of each item.
In this case, n = 6 (total number of letters) and r_1 = 2 (repetitions of letter O).
So, the number of ways the letters of the word SOKOTO can be permuted = P(6; 2) = 6!/(2!) = (6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) = 720/2 = 360.
Therefore, there are 360 ways to permute the letters of the word SOKOTO.
To find the number of ways the letters of the word SOKOTO can be permuted, we need to determine the total number of arrangements of the letters.
The word SOKOTO has 6 letters, with repeated letters. In this case, we calculate the permutation using the formula:
Permutation = (total number of letters)! / (frequency of repetition of each letter)!
Let's calculate it step by step:
1. Determine the total number of letters:
The word SOKOTO has 6 letters.
2. Determine the frequency of repetition of each letter:
In SOKOTO, the letter O appears twice. The other letters (S, K, and T) appear only once.
3. Plug the values into the formula:
Permutation = (6)! / (2)!
Simplifying the factorial:
Permutation = 6 * 5 * 4 * 3 * 2 * 1 / (2 * 1)
Cancel out the common factors:
Permutation = 6 * 5 * 4 * 3
4. Calculate the result:
Permutation = 360
Therefore, the letters of the word SOKOTO can be permuted in 360 different ways.