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.
How many permutations of the letters in the name BARBARA are there?
3 answers
AAAaannndd the bot gets it wrong yet again!
7!/(2!2!3!) = 210
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 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.
1 answer