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What is the number of four-digit decimal numbers (<1) in which no digit is repeated?
- a)3024
- b)4536
- c)5040
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the number of four-digit decimal numbers (<1) in which no d...
Let the given 4 digit decimal number is 
Places after decimal can be filled in the following ways:
Total number of ways = 7 x 8 x 9 x 9 = 4536
Places after decimal can be filled in the following ways:
Total number of ways = 7 x 8 x 9 x 9 = 4536
Most Upvoted Answer
What is the number of four-digit decimal numbers (<1) in which no d...
Counting Four-Digit Decimal Numbers with No Repeated Digits
To find the number of four-digit decimal numbers where no digit is repeated, we can follow these steps:
Step 1: Choosing the Thousands Place
- Since the number should be less than 1, the thousands place can only have digits 1, 2, or 3.
- Therefore, there are 3 choices for the thousands place.
Step 2: Choosing the Hundreds Place
- After selecting a digit for the thousands place, there are 9 digits left for the hundreds place (excluding the digit used in the thousands place).
- Hence, there are 9 choices for the hundreds place.
Step 3: Choosing the Tens Place
- After selecting digits for the thousands and hundreds places, there are 8 digits left for the tens place.
- So, there are 8 choices for the tens place.
Step 4: Choosing the Units Place
- Finally, after selecting digits for the thousands, hundreds, and tens places, there are 7 digits left for the units place.
- Thus, there are 7 choices for the units place.
Calculating the Total Number of Numbers
- To find the total number of four-digit decimal numbers meeting the given conditions, we multiply the choices for each place: 3 x 9 x 8 x 7 = 1512.
- However, since the question specifies numbers less than 1, we need to consider numbers starting from 1000 up to 9999.
- Therefore, the total number of four-digit decimal numbers less than 1 with no repeated digits is 1512 x 3 = 4536.
Therefore, the correct answer is option B) 4536.
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What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number of four-digit decimal numbers (<1) in which no digit is repeated?a)3024b)4536c)5040d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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