

Adam wrote down a 11-digit university roll number on a piece of paper. On his way home from office, it rained heavily and the paper got wet. Later, he saw that the first 2 digits of the roll number had disappeared. In how many ways can Adam complete this university roll number if repetition of digits is allowed?

To solve the problem, we need to determine how many ways Adam can reconstruct the 11-digit university roll number when the first 2 digits are missing, assuming that repetition of digits is allowed.

The original roll number is 11 digits long, but since the first 2 digits have disappeared, we are left with 9 known digits and 2 missing digits.

For each of the 2 missing digits, there are 10 possible values (0 through 9), since repetition is allowed.

To find the total number of ways to complete the roll number, we multiply the number of possibilities for each missing digit. Hence, we have:

\[
10 \times 10 = 100
\]

Therefore, Adam can complete the university roll number in \( \boxed{100} \) different ways.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How many ways can Adam complete the roll number if repetition of digits is not allowed?
2. What if the roll number had been 12 digits long instead of 11?
3. If Adam remembered that the first digit was not zero, how many ways could he then complete the roll number?
4. How does the solution change if Adam remembers one of the missing digits?
5. Can you calculate the number of ways if three digits were missing instead of two?

**Tip:** When dealing with combinatorial problems, carefully consider whether repetition of elements is allowed and whether there are any restrictions on the elements.

Learn how to calculate the number of ways Adam can complete a university roll number after losing the first 2 digits. Explore combinatorial methods and repetition rules in this mathematical problem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation