In how many distinct ways can the letters of the word robber be arranged?
The word "robber" has 6 letters.
To find the number of distinct ways the letters can be arranged, we can use the concept of permutations.
Since there are no repeated letters in the word "robber," we can find the number of arrangements by calculating 6 factorial (6!):
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Therefore, there are 720 distinct ways the letters of the word "robber" can be arranged.
To find the number of distinct ways the letters of the word "robber" can be arranged, we need to compute the number of permutations.
The word "robber" has 6 letters, but the letter 'r' occurs twice and the letter 'b' occurs twice. This means we have repeated letters, which will affect the number of distinct arrangements.
To calculate the number of distinct arrangements, we can use the formula for permutations with repeated elements:
Number of distinct arrangements = (Total number of arrangements) / (Number of repetitions of each element)
In this case, the total number of arrangements is 6!, which is the factorial of 6.
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Since the letter 'r' occurs twice and the letter 'b' occurs twice, we need to divide the total number of arrangements by the factorial of the repetitions, which is 2! for each letter.
2! = 2 * 1 = 2
Thus, the number of distinct arrangements of the word "robber" is:
Number of distinct arrangements = 720 / (2! * 2!) = 720 / (2 * 2) = 720 / 4 = 180
Therefore, the word "robber" can be arranged in 180 distinct ways.