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The number of 4 digits number formed with the digits 1,1,2,2,3,4?
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The number of 4 digits number formed with the digits 1,1,2,2,3,4?
Understanding the Problem
To find the number of unique 4-digit numbers formed from the digits 1, 1, 2, 2, 3, 4, we need to consider the repetitions of certain digits.
Available Digits
- The digits we have are: 1, 1, 2, 2, 3, 4.
- We can use each digit only as many times as it appears in the list.
Cases for Selection
We can categorize the selections based on how many of each digit we choose:
Calculating Each Case
1. Case 1: Four different digits (1, 2, 3, 4)
- Number of arrangements = 4! = 24
2. Case 2: Three of one digit, one of another
- Not possible since we don't have three of any digit.
3. Case 3: Two pairs (1, 1, 2, 2)
- Number of arrangements = 4! / (2! * 2!) = 6
4. Case 4: Two of one digit, two of another (1s and 2s)
- Not applicable as we can’t select two from 3 or 4.
Total Unique 4-Digit Numbers
Adding the cases that yield results gives us:
- Case 1: 24
- Case 2: 0
- Case 3: 6
- Total = 24 + 0 + 6 = 30
Final Result
Thus, the total number of unique 4-digit numbers that can be formed with the digits 1, 1, 2, 2, 3, and 4 is 30.
To find the number of unique 4-digit numbers formed from the digits 1, 1, 2, 2, 3, 4, we need to consider the repetitions of certain digits.
Available Digits
- The digits we have are: 1, 1, 2, 2, 3, 4.
- We can use each digit only as many times as it appears in the list.
Cases for Selection
We can categorize the selections based on how many of each digit we choose:
- Case 1: Four different digits
- Case 2: Three digits are the same, one is different
- Case 3: Two pairs of digits
- Case 4: Two of one digit and two of another
Calculating Each Case
1. Case 1: Four different digits (1, 2, 3, 4)
- Number of arrangements = 4! = 24
2. Case 2: Three of one digit, one of another
- Not possible since we don't have three of any digit.
3. Case 3: Two pairs (1, 1, 2, 2)
- Number of arrangements = 4! / (2! * 2!) = 6
4. Case 4: Two of one digit, two of another (1s and 2s)
- Not applicable as we can’t select two from 3 or 4.
Total Unique 4-Digit Numbers
Adding the cases that yield results gives us:
- Case 1: 24
- Case 2: 0
- Case 3: 6
- Total = 24 + 0 + 6 = 30
Final Result
Thus, the total number of unique 4-digit numbers that can be formed with the digits 1, 1, 2, 2, 3, and 4 is 30.
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The number of 4 digits number formed with the digits 1,1,2,2,3,4?
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The number of 4 digits number formed with the digits 1,1,2,2,3,4? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of 4 digits number formed with the digits 1,1,2,2,3,4? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of 4 digits number formed with the digits 1,1,2,2,3,4?.
The number of 4 digits number formed with the digits 1,1,2,2,3,4? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of 4 digits number formed with the digits 1,1,2,2,3,4? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of 4 digits number formed with the digits 1,1,2,2,3,4?.
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