Question

algebra 1 b-cr
pre-test complete
1 2 3 4 5 6 7
in how many ways can the letters in the word spoon be arranged?
○ 24
○ 30
○ 60
○ 120

Explanation:

Step1: Identify total letters and duplicates

The word "spoon" has 5 total letters, with 2 identical 'o's.

Step2: Apply permutation formula for duplicates

The formula for permutations of multiset is $\frac{n!}{k!}$, where $n=5$ (total letters) and $k=2$ (duplicate letters).
$$\frac{5!}{2!} = \frac{5\times4\times3\times2\times1}{2\times1}$$

Step3: Calculate the result

Simplify the expression:
$$\frac{120}{2} = 60$$

Answer:

60 (Option C: 60)