How many permutations of the letters in the name BARBARA are there?
AAAaannndd the bot gets it wrong yet again!
7!/(2!2!3!) = 210
Apologies for the incorrect response. You are right!
To calculate the number of permutations of the letters in the name BARBARA, we need to account for the repeated letters.
The name BARBARA has 7 letters, with 2 letters "B" and 2 letters "A" being repeated. We need to divide the total number of arrangements (7!) by the factorials of the frequencies of the repeated letters.
Therefore, the correct calculation is:
7! / (2! * 2! * 3!) = 7 * 6 * 5 * 4 * 3 * 2 * 1 / (2 * 1 * 2 * 1 * 3 * 2 * 1) = 210.
So, there are 210 permutations of the letters in the name BARBARA.
To find the number of permutations of the letters in the name BARBARA, we need to consider the number of each repeating letter.
In this case, we have the letter "A" repeated twice, the letter "B" repeated twice, and the letter "R" once.
To calculate the total number of permutations, we can use the formula:
Total permutations = n! / (n1! * n2! * ... * nk!)
where n is the total number of letters and n1, n2, ..., nk are the number of repetitions for each letter.
In this case, n = 7 (the total number of letters), n1 = 2 (for the letter "A"), n2 = 2 (for the letter "B"), and n3 = 1 (for the letter "R").
Using the formula, the total number of permutations is:
Total permutations = 7! / (2! * 2! * 1!)
Calculating this expression:
Total permutations = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 2 * 1)
Simplifying:
Total permutations = 5040 / 4
Total permutations = 1260
So, there are 1260 permutations of the letters in the name BARBARA.
There are 7 letters in the name BARBARA, but two of them are repeated (the letter A). To determine the number of permutations, we need to divide the total number of possible arrangements by the number of ways to arrange the repeated letters.
The total number of arrangements of 7 letters is 7!.
To determine the number of arrangements of the repeated letters, we divide by the factorial of the number of repeated letters. In this case, we divide by 2!.
Therefore, the number of permutations of the letters in the name BARBARA is 7!/2! = 7 * 6 * 5 * 4 * 3 * 2 * 1 / (2 * 1) = 7 * 6 * 5 * 4 * 3 = 3,360.