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If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _______. (in integers)
Correct answer is '96'. Can you explain this answer?
Verified Answer
If the digits are not allowed to repeat in any number formed by using ...
4 × 4 × 3 × 2 = 96Most Upvoted Answer
If the digits are not allowed to repeat in any number formed by using ...
Understanding the Problem
To find the number of integers greater than 10,000 using the digits 0, 2, 4, 6, and 8 without repetition, we need to consider five-digit numbers specifically.
Conditions for the Number
1. A five-digit number must start with a non-zero digit.
2. The digits we can use are 0, 2, 4, 6, and 8.
Choosing the First Digit
- The first digit can only be one of the non-zero digits (2, 4, 6, 8). Thus, we have 4 choices.
Choosing the Remaining Digits
- After choosing the first digit, we have 4 digits left (including 0) to fill the remaining 4 positions.
Calculating the Total Combinations
- The number of ways to arrange the remaining 4 digits is given by the permutation of selecting 4 from the remaining 4 digits.
- The calculation is as follows:
- Choose the first digit: 4 options (2, 4, 6, 8)
- Choose the second digit: 4 options (any of the remaining digits including 0)
- Choose the third digit: 3 options
- Choose the fourth digit: 2 options
- Choose the fifth digit: 1 option
Mathematical Calculation
- Total combinations = 4 (first digit choices) * 4! (permutations of remaining digits)
- 4! = 4 × 3 × 2 × 1 = 24
- Therefore, total combinations = 4 * 24 = 96.
Conclusion
The total number of five-digit numbers greater than 10,000 that can be formed using the digits 0, 2, 4, 6, and 8 without repeating any digits is 96.
To find the number of integers greater than 10,000 using the digits 0, 2, 4, 6, and 8 without repetition, we need to consider five-digit numbers specifically.
Conditions for the Number
1. A five-digit number must start with a non-zero digit.
2. The digits we can use are 0, 2, 4, 6, and 8.
Choosing the First Digit
- The first digit can only be one of the non-zero digits (2, 4, 6, 8). Thus, we have 4 choices.
Choosing the Remaining Digits
- After choosing the first digit, we have 4 digits left (including 0) to fill the remaining 4 positions.
Calculating the Total Combinations
- The number of ways to arrange the remaining 4 digits is given by the permutation of selecting 4 from the remaining 4 digits.
- The calculation is as follows:
- Choose the first digit: 4 options (2, 4, 6, 8)
- Choose the second digit: 4 options (any of the remaining digits including 0)
- Choose the third digit: 3 options
- Choose the fourth digit: 2 options
- Choose the fifth digit: 1 option
Mathematical Calculation
- Total combinations = 4 (first digit choices) * 4! (permutations of remaining digits)
- 4! = 4 × 3 × 2 × 1 = 24
- Therefore, total combinations = 4 * 24 = 96.
Conclusion
The total number of five-digit numbers greater than 10,000 that can be formed using the digits 0, 2, 4, 6, and 8 without repeating any digits is 96.
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If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _______. (in integers)Correct answer is '96'. Can you explain this answer?
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