Question
How many distinguishable arrangements are there in the word 'success '
Answers
GPT 3.5
The word "success" has 7 letters, with the letter 's' repeated 3 times and the letter 'c' repeated 2 times.
To find the number of distinguishable arrangements, we can use the formula for permutations with repeated elements:
n! / (n1! * n2! * ... * nk!)
where n is the total number of letters and n1, n2, ..., nk are the number of repetitions for each repeated letter.
In this case, n = 7, n1 = 3 (for 's') and n2 = 2 (for 'c').
Therefore, the number of distinguishable arrangements is:
7! / (3! * 2!) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1)) = 7 * 5 * 4 = 140.
So, there are 140 distinguishable arrangements in the word "success".
To find the number of distinguishable arrangements, we can use the formula for permutations with repeated elements:
n! / (n1! * n2! * ... * nk!)
where n is the total number of letters and n1, n2, ..., nk are the number of repetitions for each repeated letter.
In this case, n = 7, n1 = 3 (for 's') and n2 = 2 (for 'c').
Therefore, the number of distinguishable arrangements is:
7! / (3! * 2!) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1)) = 7 * 5 * 4 = 140.
So, there are 140 distinguishable arrangements in the word "success".