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How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?
Correct answer is '502'. Can you explain this answer?
Verified Answer
How many numbers with two or more digits can be formed with the digits...
It has been given that the digits in the number should appear in the ascending order. Therefore, there is only 1 possible arrangement of the digits once they are selected to form a number.
There are 9 numbers (1,2,3,4,5,6,7,8,9) in total. 2 digit numbers can be formed in ways. 3 digit numbers can be formed in ways. ..................................................
..9 digit number can be formed in 9C9 ways.

We have to subtract  from both the sides of the equations since we cannot form single digit numbers.

Therefore, 502 is the right answer.
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Most Upvoted Answer
How many numbers with two or more digits can be formed with the digits...
Solution:

The given problem can be solved using the concept of combinations.

Step 1: Identify the number of digits to be used
- We need to form numbers with two or more digits.
- Therefore, we can use 2, 3, 4, 5, 6, 7, 8, or 9 digits.

Step 2: Identify the digits to be used
- We have 9 digits available: 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- We need to select the digits to be used in the numbers.
- Since we need to use each digit at most once, we can select the digits using combinations.

Step 3: Identify the arrangement of the digits
- The digits must appear in ascending order in the numbers.
- Therefore, the arrangement of the digits is fixed.

Step 4: Find the number of ways to form the numbers
- For each value of n (2, 3, 4, 5, 6, 7, 8, 9), we can select n digits from the available 9 digits using combinations.
- Once the digits are selected, the arrangement is fixed.
- Therefore, the number of ways to form the numbers is equal to the number of ways to select n digits.
- The total number of ways to form the numbers is the sum of the number of ways to form the numbers using 2, 3, 4, 5, 6, 7, 8, or 9 digits.

Step 5: Calculate the number of ways to select n digits
- The number of ways to select n digits from a set of m digits is given by the formula: C(m,n) = m! / (n! * (m-n)!), where C(m,n) denotes the number of ways to select n items from a set of m items.
- Using this formula, we can calculate the number of ways to select n digits from the available 9 digits for each value of n.

Step 6: Calculate the total number of ways to form the numbers
- The total number of ways to form the numbers is the sum of the number of ways to form the numbers using 2, 3, 4, 5, 6, 7, 8, or 9 digits.
- We can calculate this sum by adding the number of ways to form the numbers using each value of n.

Step 7: Calculate the final answer
- Using the above steps, we can calculate the total number of ways to form the numbers with the given conditions.
- The final answer is 502.

Answer: The total number of numbers that can be formed with two or more digits using the digits 1,2,3,4,5,6,7,8,9, such that each digit is used at most once and the digits appear in ascending order is 502.
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How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?Correct answer is '502'. Can you explain this answer?
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