The number of ways to rearrange the letters of the word CHEESE is

Options

A. 120
B. 240
C. 720
D. 6

Answer

To find the number of ways to rearrange the letters of the word "CHEESE," we can follow these steps:

### Step 1: Identify the total number of letters and their frequencies
The word "CHEESE" consists of 6 letters. We need to identify the frequency of each letter:
- C: 1
- H: 1
- E: 3
- S: 1

### Step 2: Use the formula for permutations of multiset
The formula for the number of permutations of a multiset is given by:

\[ \text{Number of arrangements} = \frac{n!}{n_1! \times n_2! \times n_3! \times \ldots} \]

where \( n \) is the total number of items, and \( n_1, n_2, n_3, \ldots \) are the frequencies of the distinct items.

### Step 3: Apply the formula
In our case:
- Total letters \( n = 6 \)
- Frequencies are:
- E: 3
- C: 1
- H: 1
- S: 1

So, we can write:

\[ \text{Number of arrangements} = \frac{6!}{3! \times 1! \times 1! \times 1!} \]

### Step 4: Calculate the factorials
Now, we need to calculate the factorials:
- \( 6! = 720 \)
- \( 3! = 6 \)
- \( 1! = 1 \) (for C, H, and S)

### Step 5: Substitute the values into the formula
Now substituting the values into the formula:

\[ \text{Number of arrangements} = \frac{720}{6 \times 1 \times 1 \times 1} = \frac{720}{6} = 120 \]

### Final Answer
Thus, the number of ways to rearrange the letters of the word "CHEESE" is **120**.

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