Different words are being formed by arranging the letters of the word "SUCCESS".
The probability of selecting a word that begins and ends with S is

Options

A. `1/7`
B. `2/7`
C. `2/35`
D. `2/5`

Answer

To solve the problem of finding the probability of selecting a word that begins and ends with 'S' from the letters of the word "SUCCESS", we can follow these steps:

### Step 1: Identify the letters in "SUCCESS"
The word "SUCCESS" consists of the letters: S, U, C, C, E, S, S.
- Total letters = 7
- Breakdown: S (3), U (1), C (2), E (1)

### Step 2: Determine the total arrangements of the word "SUCCESS"
The total number of arrangements of the letters in "SUCCESS" can be calculated using the formula for permutations of multiset:
\[ \text{Total arrangements} = \frac{n!}{n_1! \times n_2! \times n_3!} \]
where \( n \) is the total number of letters, and \( n_1, n_2, n_3 \) are the frequencies of the distinct letters.

Here, we have:
- \( n = 7 \) (total letters)
- \( n_S = 3 \) (for S)
- \( n_C = 2 \) (for C)
- \( n_U = 1 \) (for U)
- \( n_E = 1 \) (for E)

Thus, the total arrangements are:
\[ \text{Total arrangements} = \frac{7!}{3! \times 2! \times 1! \times 1!} = \frac{5040}{6 \times 2 \times 1 \times 1} = \frac{5040}{12} = 420 \]

### Step 3: Calculate the favorable arrangements that start and end with 'S'
When a word starts and ends with 'S', we can fix 'S' at the beginning and 'S' at the end. This leaves us with the letters: U, C, C, E, S (5 letters).

Now we need to arrange these 5 letters:
- Letters to arrange: U, C, C, E, S
- The number of arrangements is given by:
\[ \text{Favorable arrangements} = \frac{5!}{2! \times 1! \times 1! \times 1!} = \frac{120}{2} = 60 \]

### Step 4: Calculate the probability
The probability of selecting a word that begins and ends with 'S' is given by the ratio of favorable arrangements to total arrangements:
\[ \text{Probability} = \frac{\text{Favorable arrangements}}{\text{Total arrangements}} = \frac{60}{420} = \frac{1}{7} \]

### Final Answer
The probability of selecting a word that begins and ends with 'S' is \( \frac{1}{7} \).

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