Numbers with distinct digits from 1000-9999

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In summary, there are 4536 numbers with distinct digits from 1000 to 9999, and 2240 odd numbers with distinct digits from 1000 to 9999. This is determined by the available choices for each place value and the restriction of having only odd numbers for the units place.
  • #1
jonroberts74
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Homework Statement



A) how many numbers have distinct digits from 1000 to 9999?

B) how many odd numbers have distinct digits from 1000 to 9999?





The Attempt at a Solution



a) the first place value has choices from 1-9, the second has choices from 0-9 but one number was used in the first place value so it has 9 choices, third place has 8 choices and fourth place has 7 choices so

9*9*8*7 numbers = 4536 numbers with distinct digits

b)

the available digits are 1,3,5,7,9

so first place has 5 choices, second has 4, third has 3, fourth has 2

so 5*4*3*2 numbers = 120 odd numbers with distinct digits.

that question seemed a little too easy so that's why I am posting it.
 
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  • #2
Part (a) is correct, but (b) is not. You have solved the case where each digit of the number is odd, however, the question asks for odd numbers, which means only the last digit will be odd.
 
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  • #3
Infinitum said:
Part (a) is correct, but (b) is not. You have solved the case where each digit of the number is odd, however, the question asks for odd numbers, which means only the last digit will be odd.

ah okay, that makes

sense so 9*9*8*5 numbers = 3240 numbers with distinct digits that are odd.
 
  • #4
Not quite. You already decided to reserve an odd digit for the units place, and you cannot have zero in the first digit. How many possibilities does that leave for the first digit? Apply the argument further to the second and third digits.
 
  • #5
so first will have 8 choices, second will have 8 because there's the reserved digit and the digit used in the first place but now zero is available, so third will have 7 and the fourth has 5

8*8*7*5 = 2240 numbers
 
  • #6
Yep, that's it! :approve:
 

FAQ: Numbers with distinct digits from 1000-9999

1. What are numbers with distinct digits from 1000-9999?

Numbers with distinct digits from 1000-9999 are four-digit numbers where each digit is unique and does not repeat.

2. How many numbers with distinct digits are there from 1000-9999?

There are 9 x 9 x 8 x 7 = 4536 numbers with distinct digits from 1000-9999. This can be calculated by multiplying the number of choices for each digit (9 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit).

3. Are there any special properties of numbers with distinct digits from 1000-9999?

Numbers with distinct digits from 1000-9999 are often used in mathematical puzzles and games, as they have a unique and ordered structure. They are also useful in coding and cryptography, as they can be used as unique identifiers.

4. How can I generate a list of numbers with distinct digits from 1000-9999?

To generate a list of numbers with distinct digits from 1000-9999, you can use a programming language like Python to loop through all possible combinations and check if they meet the criteria of having distinct digits. Alternatively, you can use a mathematical approach to calculate and list out all possible combinations.

5. Can numbers with distinct digits from 1000-9999 be used in real-world applications?

Yes, numbers with distinct digits from 1000-9999 can be used in various real-world applications such as phone numbers, social security numbers, and bank account numbers. They can also be used in data encryption and identification systems.

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