Count each 7 which is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 7's are there? 5 7 2 6 5 7 3 8 3 7 3 2 5 7 2 7 3 4 8 2 6 7 8

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To solve the problem, we need to count the occurrences of the number 7 in the given sequence based on specific conditions. The conditions are that the 7 must not be immediately preceded by 5 and must be immediately followed by either 2 or 3.

Let's analyze the sequence step by step:

**Given Sequence:**
5, 7, 2, 6, 5, 7, 3, 8, 3, 7, 3, 2, 5, 7, 2, 7, 3, 4, 8, 2, 6, 7, 8

**Step 1: Identify each 7 and check the conditions.**

1. **First 7 (5, 7, 2)**:
- Preceded by 5 (not allowed)
- Not counted.

2. **Second 7 (5, 7, 3)**:
- Preceded by 5 (not allowed)
- Not counted.

3. **Third 7 (8, 3, 7, 3, 2)**:
- Preceded by 3 (allowed)
- Followed by 3 (allowed)
- Counted.

4. **Fourth 7 (5, 7, 2)**:
- Preceded by 5 (not allowed)
- Not counted.

5. **Fifth 7 (2, 7, 3)**:
- Preceded by 2 (allowed)
- Followed by 3 (allowed)
- Counted.

6. **Sixth 7 (4, 8, 2, 6, 7, 8)**:
- Preceded by 6 (allowed)
- Followed by 8 (not allowed)
- Not counted.

**Step 2: Count the valid 7s.**

From our analysis, we found:
- Valid 7s: 1 (from 3, 7, 3) and 2 (from 2, 7, 3).

**Final Count: 2**

Thus, the total number of 7s that meet the criteria is **2**.

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