Find the number of ways to arrange the letters in CANADIAN.

To find the number of ways to arrange the letters in "CANADIAN," we start by recognizing that this word consists of 8 letters, where certain letters repeat. The breakdown is: - C: 1 - A: 2 - N: 2 - D: 1 - I: 1 The formula for calculating the number of arrangements of letters where some letters are repeated is given by: \[ \text{Number of arrangements} = \frac{n!}{p_1! \times p_2! \times \ldots \times p_k!} \] where \( n \) is the total number of letters, and \( p_1, p_2, \ldots, p_k \) are the frequencies of the repeated letters. For "CANADIAN": - Total letters (n) = 8 - Frequencies: A occurs 2 times, N occurs 2 times So, we compute: \[ \text{Number of arrangements} = \frac{8!}{2! \times 2!} \] First, we calculate \( 8! \): \[ 8! = 40320 \] Next, calculate \( 2! \): \[ 2! = 2 \] Now plug these into the formula: \[ \text{Number of arrangements} = \frac{40320}{2 \times 2} = \frac{40320}{4} = 10080 \] Thus, the number of ways to arrange the letters in "CANADIAN" is **10,080**.