Question

problem b
in how many ways can the letters of the word \canada\ be arranged?

Explanation:

Step1: Identify repeated letters

The word "CANADA" has 6 letters. The letter 'A' appears 3 times, and the letter 'N' appears 1 time, 'C' appears 1 time, 'D' appears 1 time.

Step2: Use permutation formula for repeated elements

The formula for permutations of a word with repeated elements is $\frac{n!}{n_1!n_2!...n_k!}$, where $n$ is the total number of elements, and $n_1,n_2,...,n_k$ are the number of times each repeated element appears. Here, $n = 6$, $n_1 = 3$ (for 'A').

Step3: Calculate factorials

$6! = 6\times5\times4\times3\times2\times1 = 720$, $3! = 3\times2\times1 = 6$.

Step4: Compute the result

$\frac{6!}{3!} = \frac{720}{6} = 120$.

Answer:

120