The number of 5-digit numbers in which no two consecutive digits are identical, is

Options

A. `9^(2)xx8^(3)`
B. `9xx8^(4)`
C. `9^(5)`
D. none of these

Explanation

To solve the problem of finding the number of 5-digit numbers in which no two consecutive digits are identical, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the first digit:**
- The first digit of a 5-digit number cannot be 0 (as it would then be a 4-digit number). Therefore, the possible choices for the first digit are from 1 to 9.
- **Number of options for the first digit:** 9 (choices: 1, 2, 3, 4, 5, 6, 7, 8, 9).

2. **Identify the second digit:**
- The second digit can be any digit from 0 to 9, except for the digit chosen as the first digit (to ensure no two consecutive digits are identical).
- **Number of options for the second digit:** 9 (choices: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 minus the first digit).

3. **Identify the third digit:**
- The third digit can also be any digit from 0 to 9, except for the digit chosen as the second digit.
- **Number of options for the third digit:** 9.

4. **Identify the fourth digit:**
- The fourth digit follows the same rule and can be any digit from 0 to 9, except for the digit chosen as the third digit.
- **Number of options for the fourth digit:** 9.

5. **Identify the fifth digit:**
- The fifth digit can be any digit from 0 to 9, except for the digit chosen as the fourth digit.
- **Number of options for the fifth digit:** 9.

6. **Calculate the total number of valid 5-digit numbers:**
- The total number of ways to form the 5-digit number is the product of the number of options for each digit:
\[ \text{Total} = 9 \times 9 \times 9 \times 9 \times 9 = 9^5 \]

7. **Final Calculation:**
- Calculate \(9^5\):
\[ 9^5 = 59049 \]

### Final Answer:
The number of 5-digit numbers in which no two consecutive digits are identical is **59049**.

---