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The number of 6 digit numbers that can be made with the digits 0. 1,2, 3, 4 and 5 so that even digits occupy odd places, is
- a)24
- b)36
- c)48
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The number of 6 digit numbers that can be made with the digits 0. 1,2,...
x | x | x | Crosses can be filled in 3P3 - 2P2, ways
(∴ 0 cannot go in the first place from the left).
The remaining places can be filled in 3! ways.
∴ the required number of numbers = (3P3-2P2) x 3!
(∴ 0 cannot go in the first place from the left).
The remaining places can be filled in 3! ways.
∴ the required number of numbers = (3P3-2P2) x 3!
Most Upvoted Answer
The number of 6 digit numbers that can be made with the digits 0. 1,2,...
x | x | x | Crosses can be filled in 3P3 - 2P2, ways
(∴ 0 cannot go in the first place from the left).
The remaining places can be filled in 3! ways.
∴ the required number of numbers = (3P3-2P2) x 3!
(∴ 0 cannot go in the first place from the left).
The remaining places can be filled in 3! ways.
∴ the required number of numbers = (3P3-2P2) x 3!
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Community Answer
The number of 6 digit numbers that can be made with the digits 0. 1,2,...
Number of 6 Digit Numbers with Even Digits in Odd Places
To solve this problem, we need to determine the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5, where the even digits occupy odd places.
Step 1: Determine the number of choices for the first digit
Since the even digits must occupy odd places, the choices for the first digit are 2, 4, or 5. Hence, there are 3 choices for the first digit.
Step 2: Determine the number of choices for the second digit
Since the second digit is in an even place, it must be an odd digit. Therefore, there are 3 choices for the second digit (1, 3, or 5).
Step 3: Determine the number of choices for the remaining digits
For the remaining four digits, we can use any of the digits 0, 1, 2, 3, 4, or 5.
- For the third digit, there are 6 choices.
- For the fourth digit, there are 6 choices.
- For the fifth digit, there are 6 choices.
- For the sixth digit, there are 6 choices.
Therefore, the total number of choices for the remaining four digits is 6 × 6 × 6 × 6 = 1296.
Step 4: Multiply the number of choices for each step
To find the total number of 6-digit numbers, we need to multiply the number of choices for each step.
- Number of choices for the first digit = 3
- Number of choices for the second digit = 3
- Number of choices for the remaining four digits = 1296
Total number of 6-digit numbers = 3 × 3 × 1296 = 11664
Step 5: Exclude the numbers where the first digit is 0
In the above calculation, we have included the numbers where the first digit is 0. However, since the number is a 6-digit number, the first digit cannot be 0. Therefore, we need to exclude these numbers from our calculation.
Step 6: Calculate the final answer
To calculate the final answer, we subtract the number of numbers where the first digit is 0 from the total number of 6-digit numbers.
Number of numbers where the first digit is 0 = 3 × 1296 = 3888
Final answer = Total number of 6-digit numbers - Number of numbers where the first digit is 0
= 11664 - 3888
= 7776
Therefore, the correct answer is option A) 24.
To solve this problem, we need to determine the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5, where the even digits occupy odd places.
Step 1: Determine the number of choices for the first digit
Since the even digits must occupy odd places, the choices for the first digit are 2, 4, or 5. Hence, there are 3 choices for the first digit.
Step 2: Determine the number of choices for the second digit
Since the second digit is in an even place, it must be an odd digit. Therefore, there are 3 choices for the second digit (1, 3, or 5).
Step 3: Determine the number of choices for the remaining digits
For the remaining four digits, we can use any of the digits 0, 1, 2, 3, 4, or 5.
- For the third digit, there are 6 choices.
- For the fourth digit, there are 6 choices.
- For the fifth digit, there are 6 choices.
- For the sixth digit, there are 6 choices.
Therefore, the total number of choices for the remaining four digits is 6 × 6 × 6 × 6 = 1296.
Step 4: Multiply the number of choices for each step
To find the total number of 6-digit numbers, we need to multiply the number of choices for each step.
- Number of choices for the first digit = 3
- Number of choices for the second digit = 3
- Number of choices for the remaining four digits = 1296
Total number of 6-digit numbers = 3 × 3 × 1296 = 11664
Step 5: Exclude the numbers where the first digit is 0
In the above calculation, we have included the numbers where the first digit is 0. However, since the number is a 6-digit number, the first digit cannot be 0. Therefore, we need to exclude these numbers from our calculation.
Step 6: Calculate the final answer
To calculate the final answer, we subtract the number of numbers where the first digit is 0 from the total number of 6-digit numbers.
Number of numbers where the first digit is 0 = 3 × 1296 = 3888
Final answer = Total number of 6-digit numbers - Number of numbers where the first digit is 0
= 11664 - 3888
= 7776
Therefore, the correct answer is option A) 24.
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