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How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]
- a)25
- b)60
- c)75
- d)100
- e)15
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
How many three-digit odd numbers can be formed from the digits 1, 3, 5...
To find out how many three-digit odd numbers can be formed from the digits 1, 3, 5, 0, and 8, we need to consider the constraints:
- The number must be three digits long.
- It must be odd.
- We can use the digits 1, 3, 5, 0, and 8.
For a number to be odd, its last digit must be odd. Given the digits, we have three choices for the last digit (1, 3, 5) to ensure the number is odd.
For the first digit, we can choose any of the four digits except 0 (because a three-digit number cannot start with 0). This gives us 4 options (1, 3, 5, 8).
For the middle digit, we can choose any of the remaining four digits (after choosing the first and the last, but remembering digits can be reused because it's not specified that digits cannot repeat). This gives us 5 options since all five digits are available for use again.
Therefore, the total number of possible three-digit odd numbers is given by the product of the number of options for each position, which is 4×5×34×5×3.
Let's calculate this:
The total number of three-digit odd numbers that can be formed from the digits 1, 3, 5, 0, and 8 is 60. Therefore, the correct answer is option 2: 60.
Most Upvoted Answer
How many three-digit odd numbers can be formed from the digits 1, 3, 5...
Solution:
Firstly, we need to determine the total number of three-digit numbers that can be formed using the given digits. This can be done by using the fundamental principle of counting, which states that if there are m ways of doing one thing and n ways of doing another thing, then there are m x n ways of doing both.
Using this principle, we can determine the total number of three-digit numbers that can be formed using the given digits as follows:
- For the first digit, we have 5 choices (1, 3, 5, 0, or 8).
- For the second digit, we have 5 choices again (since we can repeat digits).
- For the third digit, we have 5 choices again.
Therefore, the total number of three-digit numbers that can be formed using the given digits is:
5 x 5 x 5 = 125
However, we want to find only the odd three-digit numbers. This means that the last digit must be either 1, 3, or 5.
Using the same principle of counting, we can determine the number of odd three-digit numbers that can be formed using the given digits as follows:
- For the first digit, we have 5 choices (1, 3, 5, 0, or 8).
- For the second digit, we have 5 choices again.
- For the third digit, we have only 3 choices (1, 3, or 5).
Therefore, the total number of odd three-digit numbers that can be formed using the given digits is:
5 x 5 x 3 = 75
Hence, the correct answer is option (c) 75.
Firstly, we need to determine the total number of three-digit numbers that can be formed using the given digits. This can be done by using the fundamental principle of counting, which states that if there are m ways of doing one thing and n ways of doing another thing, then there are m x n ways of doing both.
Using this principle, we can determine the total number of three-digit numbers that can be formed using the given digits as follows:
- For the first digit, we have 5 choices (1, 3, 5, 0, or 8).
- For the second digit, we have 5 choices again (since we can repeat digits).
- For the third digit, we have 5 choices again.
Therefore, the total number of three-digit numbers that can be formed using the given digits is:
5 x 5 x 5 = 125
However, we want to find only the odd three-digit numbers. This means that the last digit must be either 1, 3, or 5.
Using the same principle of counting, we can determine the number of odd three-digit numbers that can be formed using the given digits as follows:
- For the first digit, we have 5 choices (1, 3, 5, 0, or 8).
- For the second digit, we have 5 choices again.
- For the third digit, we have only 3 choices (1, 3, or 5).
Therefore, the total number of odd three-digit numbers that can be formed using the given digits is:
5 x 5 x 3 = 75
Hence, the correct answer is option (c) 75.
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Community Answer
How many three-digit odd numbers can be formed from the digits 1, 3, 5...
As it is three digit odd numbers only (1,3,5) can be placed in unit digit and in tenth place all the five digits(1,3,5,0,8) can be placed and in hundredth place only four digits(1,3,5,8) can be placed ..as repetition of numbers is allowed the numbers of 3 digits numbers can be formed is (3×5×4=60)
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How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]a)25b)60c)75d)100e)15Correct answer is option 'B'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]a)25b)60c)75d)100e)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]a)25b)60c)75d)100e)15Correct answer is option 'B'. Can you explain this answer?.
How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]a)25b)60c)75d)100e)15Correct answer is option 'B'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]a)25b)60c)75d)100e)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8? [repetition is allowed ]a)25b)60c)75d)100e)15Correct answer is option 'B'. Can you explain this answer?.
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