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The number of four-digit number greater than or equal to 4321 that can be formed from the digit 0,1,2,3,4,5 allowing for repetition of digits is
- a)360
- b)310
- c)313
- d)311
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The number of four-digit number greater than or equal to 4321 that can...
If the number is in 5 thousands, there are 6x6x6 ways of choosing it.
If the number is in 4 thousands 4 hundreds there are 2x6x6 ways of choosing it.
If the number is in 4 thousand 3 hundreds, there are 3 x 6 + 5 ways of choosing it.
So, total ways = 6x6x6 + 2x6x6 + 3x6 + 5 = 311
Most Upvoted Answer
The number of four-digit number greater than or equal to 4321 that can...
Counting Four-Digit Numbers
To form a four-digit number greater than or equal to 4321 using the digits 0, 1, 2, 3, 4, and 5, we need to consider the following:
Thousands Place
- Since the number has to be greater than or equal to 4321, the thousands place can only be filled with 4 or 5 (2 options).
Hundreds Place
- For the hundreds place, any of the six digits can be used (6 options).
Tens Place
- Similarly, any of the six digits can be used for the tens place (6 options).
Ones Place
- Finally, any of the six digits can be used for the ones place as well (6 options).
Total Number of Four-Digit Numbers
- Multiplying the number of options for each place, we get: 2 (thousands place) x 6 (hundreds place) x 6 (tens place) x 6 (ones place) = 432.
Therefore, the total number of four-digit numbers that can be formed from the given digits is 432.
Numbers Starting with 0
- If the number starts with 0, it will not be greater than or equal to 4321.
- The only possibility is numbers starting with 1, 2, 3, 4, or 5.
Final Answer
- Subtracting the numbers starting with 0 from the total count, we get: 432 - 1 = 431.
- Hence, the number of four-digit numbers greater than or equal to 4321 that can be formed from the digits 0, 1, 2, 3, 4, 5 allowing for repetition of digits is 431.
Therefore, the correct answer is option 'D' (431).
To form a four-digit number greater than or equal to 4321 using the digits 0, 1, 2, 3, 4, and 5, we need to consider the following:
Thousands Place
- Since the number has to be greater than or equal to 4321, the thousands place can only be filled with 4 or 5 (2 options).
Hundreds Place
- For the hundreds place, any of the six digits can be used (6 options).
Tens Place
- Similarly, any of the six digits can be used for the tens place (6 options).
Ones Place
- Finally, any of the six digits can be used for the ones place as well (6 options).
Total Number of Four-Digit Numbers
- Multiplying the number of options for each place, we get: 2 (thousands place) x 6 (hundreds place) x 6 (tens place) x 6 (ones place) = 432.
Therefore, the total number of four-digit numbers that can be formed from the given digits is 432.
Numbers Starting with 0
- If the number starts with 0, it will not be greater than or equal to 4321.
- The only possibility is numbers starting with 1, 2, 3, 4, or 5.
Final Answer
- Subtracting the numbers starting with 0 from the total count, we get: 432 - 1 = 431.
- Hence, the number of four-digit numbers greater than or equal to 4321 that can be formed from the digits 0, 1, 2, 3, 4, 5 allowing for repetition of digits is 431.
Therefore, the correct answer is option 'D' (431).
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The number of four-digit number greater than or equal to 4321 that can be formed from the digit 0,1,2,3,4,5 allowing for repetition of digits isa)360b)310c)313d)311Correct answer is option 'D'. Can you explain this answer?
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