Math Problem Statement

how many 2-digit numbers can be formed 1 to 9 without repetition

Solution

To find how many two-digit numbers can be formed using the digits from 1 to 9 without repetition, follow these steps:

  1. Choose the first digit: The first digit can be any digit from 1 to 9, so there are 9 possible choices.

  2. Choose the second digit: Since repetition is not allowed, once the first digit is chosen, there are only 8 remaining digits for the second place.

Therefore, the total number of two-digit numbers is:

9×8=729 \times 8 = 72

Thus, 72 two-digit numbers can be formed from the digits 1 to 9 without repetition.

Would you like more details on this calculation or any further clarification?

Here are 5 related questions:

  1. How would the answer change if repetition of digits were allowed?
  2. How many 3-digit numbers can be formed using digits from 1 to 9 without repetition?
  3. What if the digits could range from 0 to 9 instead of just 1 to 9? How does that affect the total number of two-digit numbers?
  4. If we wanted to form a two-digit number but could not use a specific digit (like 5), how would we calculate that?
  5. What is the total number of combinations if we want to form a 4-digit number using digits from 1 to 9 without repetition?

Tip: When forming numbers without repetition, it's important to subtract already chosen digits from the available options at each step.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Combinatorics
Permutations

Formulas

nPr = n! / (n - r)!

Theorems

Fundamental Theorem of Counting

Suitable Grade Level

Grades 5-7