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How many four-digit numbers are there with distinct digits?
- a)6547
- b)10000
- c)3600
- d)4536
- e)5040
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
How many four-digit numbers are there with distinct digits?a)6547b)100...
4536
Hence by the fundamental counting principle, The number of 4-digit numbers are 9.9. 8.7= 4536. Therefore, there are 4536 four-digit numbers with distinct digits.
Hence by the fundamental counting principle, The number of 4-digit numbers are 9.9. 8.7= 4536. Therefore, there are 4536 four-digit numbers with distinct digits.
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How many four-digit numbers are there with distinct digits?a)6547b)100...
Problem:
How many four-digit numbers are there with distinct digits?
Solution:
To find the number of four-digit numbers with distinct digits, we need to consider the possible choices for each digit.
Step 1: Choose the thousands digit
Since it is a four-digit number, the thousands digit cannot be zero.
- We have 9 choices for the thousands digit (1-9), as zero is not allowed.
Step 2: Choose the hundreds digit
After choosing the thousands digit, we have 9 remaining digits to choose from (0-9 excluding the thousands digit).
- We have 9 choices for the hundreds digit.
Step 3: Choose the tens digit
After choosing the thousands and hundreds digits, we have 8 remaining digits to choose from.
- We have 8 choices for the tens digit.
Step 4: Choose the units digit
After choosing the thousands, hundreds, and tens digits, we have 7 remaining digits to choose from.
- We have 7 choices for the units digit.
Step 5: Multiply the choices
To find the total number of four-digit numbers with distinct digits, we multiply the choices from each step.
- Total number of four-digit numbers = 9 * 9 * 8 * 7 = 4536
Therefore, the correct answer is option D, 4536.
How many four-digit numbers are there with distinct digits?
Solution:
To find the number of four-digit numbers with distinct digits, we need to consider the possible choices for each digit.
Step 1: Choose the thousands digit
Since it is a four-digit number, the thousands digit cannot be zero.
- We have 9 choices for the thousands digit (1-9), as zero is not allowed.
Step 2: Choose the hundreds digit
After choosing the thousands digit, we have 9 remaining digits to choose from (0-9 excluding the thousands digit).
- We have 9 choices for the hundreds digit.
Step 3: Choose the tens digit
After choosing the thousands and hundreds digits, we have 8 remaining digits to choose from.
- We have 8 choices for the tens digit.
Step 4: Choose the units digit
After choosing the thousands, hundreds, and tens digits, we have 7 remaining digits to choose from.
- We have 7 choices for the units digit.
Step 5: Multiply the choices
To find the total number of four-digit numbers with distinct digits, we multiply the choices from each step.
- Total number of four-digit numbers = 9 * 9 * 8 * 7 = 4536
Therefore, the correct answer is option D, 4536.
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How many four-digit numbers are there with distinct digits?a)6547b)10000c)3600d)4536e)5040Correct answer is option 'D'. Can you explain this answer?
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