How many 5s are there in the following sequence which are immediately followed by 3 but not immediately preceded by 7?
8 9 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 3 5 7 3 8

Options

A. one
B. Two
C. Three
D. Four

Explanation

To solve the problem, we need to analyze the sequence of numbers and identify how many times the number 5 is followed by the number 3, while ensuring that it is not preceded by the number 7.

Let's break down the solution step by step:

### Step 1: Write down the sequence
The given sequence is:
8, 9, 5, 3, 2, 5, 3, 8, 5, 5, 6, 8, 7, 3, 3, 5, 7, 7, 5, 3, 6, 5, 3, 3, 5, 7, 3, 8

### Step 2: Identify the positions of 5s followed by 3
We will go through the sequence and check each occurrence of 5 to see if it is followed by 3.

- **Position 3:** 5 is followed by 3 (8, 9, 5, 3) - Valid
- **Position 6:** 5 is followed by 3 (5, 3) - Valid
- **Position 9:** 5 is followed by 6 (5, 6) - Not valid
- **Position 10:** 5 is followed by 6 (5, 6) - Not valid
- **Position 15:** 5 is followed by 7 (5, 7) - Not valid
- **Position 19:** 5 is followed by 3 (5, 3) - Valid
- **Position 22:** 5 is followed by 3 (5, 3) - Valid

### Step 3: Check the preceding number
Now, we need to ensure that each valid 5 is not preceded by 7.

1. **For the first valid 5 (Position 3):** Preceded by 9 - Valid
2. **For the second valid 5 (Position 6):** Preceded by 2 - Valid
3. **For the third valid 5 (Position 19):** Preceded by 7 - Not valid
4. **For the fourth valid 5 (Position 22):** Preceded by 6 - Valid

### Step 4: Count the valid occurrences
From our checks, the valid occurrences of 5 followed by 3 and not preceded by 7 are:
- 5 at Position 3 (preceded by 9)
- 5 at Position 6 (preceded by 2)
- 5 at Position 22 (preceded by 6)

Thus, there are **3 valid occurrences**.

### Final Answer
The total number of 5s that are immediately followed by 3 but not immediately preceded by 7 is **3**.

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