In how many distinct ways can the letters of the word ROBBERS be arranged? \( \square \) ways (Type a whole number.)

To find the number of distinct arrangements of the letters in the word "ROBBERS", we first note that it consists of 7 letters where the letter "R" appears twice and the letter "B" appears twice. The formula for the number of distinct permutations of letters in a word is given by: \[ \text{Number of arrangements} = \frac{n!}{n_1! \cdot n_2! \cdot \ldots \cdot n_k!} \] where \( n \) is the total number of letters and \( n_1, n_2, \ldots, n_k \) are the frequencies of the distinct letters. Here, we have: - Total letters, \( n = 7 \) - "R" appears 2 times, "B" appears 2 times, and "O", "E", "S" appear 1 time each. Thus, we calculate: \[ \text{Number of arrangements} = \frac{7!}{2! \cdot 2! \cdot 1! \cdot 1! \cdot 1!} \] Calculating factorials, we have: - \( 7! = 5040 \) - \( 2! = 2 \) Hence, \[ \text{Number of arrangements} = \frac{5040}{2 \cdot 2 \cdot 1 \cdot 1 \cdot 1} = \frac{5040}{4} = 1260 \] So, the number of distinct arrangements of the letters in "ROBBERS" is \( 1260 \) ways.