In how many ways, the letters of the word 'STRESS' can be arranged?

Options

A. 360
B. 240
C. 720
D. 120

Answer

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

### Step 1: Identify the letters in the word
The word "STRESS" consists of the following letters:
- S (appears 3 times)
- T (appears 1 time)
- R (appears 1 time)
- E (appears 1 time)

### Step 2: Count the total number of letters
The total number of letters in the word "STRESS" is 6.

### Step 3: Use the formula for permutations of multiset
The formula for the number of arrangements of a word with repeated letters 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 letters,
- \( n_1, n_2, n_3, \ldots \) are the frequencies of the repeated letters.

### Step 4: Apply the formula
In our case:
- Total letters \( n = 6 \)
- Frequency of S \( n_1 = 3 \)
- Frequency of T \( n_2 = 1 \)
- Frequency of R \( n_3 = 1 \)
- Frequency of E \( n_4 = 1 \)

So, we can substitute these values into the formula:

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

### Step 5: Calculate the factorials
Now we calculate the factorials:
- \( 6! = 720 \)
- \( 3! = 6 \)
- \( 1! = 1 \) (for T, R, and E)

### Step 6: Substitute and simplify
Now we substitute these values back into the equation:

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

### Step 7: Conclusion
Thus, the number of ways to arrange the letters of the word "STRESS" is **120**.

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