Quant Exam > Quant Questions > How many even numbers of four digits can be f...
Start Learning for Free
How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?
- a)648
- b)180
- c)1296
- d)600
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
How many even numbers of four digits can be formed with the digits 1, ...
The number of numbers formed would be given by 5 x 4 x 3 (given that the first digit can be filled in 5 ways, the second in 4 ways and the third in 3 ways - MNP rule).
Most Upvoted Answer
How many even numbers of four digits can be formed with the digits 1, ...
To form a four-digit number, we need to consider the following cases:
Case 1: The thousands digit is even.
In this case, we have three choices for the thousands digit: 2, 4, or 6. After selecting the thousands digit, we have six choices for each of the remaining three digits. Thus, the total number of possibilities for this case is 3 * 6 * 6 * 6 = 648.
Case 2: The thousands digit is odd.
In this case, we have two choices for the thousands digit: 1 or 3. After selecting the thousands digit, we have six choices for each of the remaining three digits. Thus, the total number of possibilities for this case is 2 * 6 * 6 * 6 = 432.
Therefore, the total number of even four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 648.
Explanation of each case:
1. The Thousands Digit is Even:
- In this case, we have three choices for the thousands digit: 2, 4, or 6.
- After selecting the thousands digit, we have six choices for each of the remaining three digits.
- This is because we can choose any of the digits 1, 2, 3, 4, 5, or 6 for each of the units, tens, and hundreds places.
- Thus, the total number of possibilities for this case is 3 * 6 * 6 * 6 = 648.
2. The Thousands Digit is Odd:
- In this case, we have two choices for the thousands digit: 1 or 3.
- After selecting the thousands digit, we have six choices for each of the remaining three digits.
- This is because we can choose any of the digits 1, 2, 3, 4, 5, or 6 for each of the units, tens, and hundreds places.
- Thus, the total number of possibilities for this case is 2 * 6 * 6 * 6 = 432.
Total Number of Possibilities:
- To find the total number of even four-digit numbers, we add the possibilities from both cases.
- Therefore, the total number of even four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 648 (648 + 432 = 1080).
Case 1: The thousands digit is even.
In this case, we have three choices for the thousands digit: 2, 4, or 6. After selecting the thousands digit, we have six choices for each of the remaining three digits. Thus, the total number of possibilities for this case is 3 * 6 * 6 * 6 = 648.
Case 2: The thousands digit is odd.
In this case, we have two choices for the thousands digit: 1 or 3. After selecting the thousands digit, we have six choices for each of the remaining three digits. Thus, the total number of possibilities for this case is 2 * 6 * 6 * 6 = 432.
Therefore, the total number of even four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 648.
Explanation of each case:
1. The Thousands Digit is Even:
- In this case, we have three choices for the thousands digit: 2, 4, or 6.
- After selecting the thousands digit, we have six choices for each of the remaining three digits.
- This is because we can choose any of the digits 1, 2, 3, 4, 5, or 6 for each of the units, tens, and hundreds places.
- Thus, the total number of possibilities for this case is 3 * 6 * 6 * 6 = 648.
2. The Thousands Digit is Odd:
- In this case, we have two choices for the thousands digit: 1 or 3.
- After selecting the thousands digit, we have six choices for each of the remaining three digits.
- This is because we can choose any of the digits 1, 2, 3, 4, 5, or 6 for each of the units, tens, and hundreds places.
- Thus, the total number of possibilities for this case is 2 * 6 * 6 * 6 = 432.
Total Number of Possibilities:
- To find the total number of even four-digit numbers, we add the possibilities from both cases.
- Therefore, the total number of even four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 648 (648 + 432 = 1080).
Free Test
FREE
| Start Free Test |
Community Answer
How many even numbers of four digits can be formed with the digits 1, ...
The answer should be 60, i.e., 5x4x3
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer?
Question Description
How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer?.
How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer?.
Solutions for How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer?, a detailed solution for How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)?a)648b)180c)1296d)600Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup