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:
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Choose the first digit: The first digit can be any digit from 1 to 9, so there are 9 possible choices.
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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:
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:
- How would the answer change if repetition of digits were allowed?
- How many 3-digit numbers can be formed using digits from 1 to 9 without repetition?
- 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?
- If we wanted to form a two-digit number but could not use a specific digit (like 5), how would we calculate that?
- 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.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations
Formulas
nPr = n! / (n - r)!
Theorems
Fundamental Theorem of Counting
Suitable Grade Level
Grades 5-7
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