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What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?
- a)2664
- b)3882
- c)4044
- d)4444
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the sum of all three-digit numbers that can be formed using al...
543 + 534 + 453 + 435 + 354 + 345 = 2664
(or)
The total such numbers possible = 6. Each of 3, 4 and 5 will appear twice in the hundredth, tenth and unit place.
Sum = 2((300 + 400 + 500) + (30 + 40 + 50) + (3 + 4 + 5)) = 2664
(or)
The total such numbers possible = 6. Each of 3, 4 and 5 will appear twice in the hundredth, tenth and unit place.
Sum = 2((300 + 400 + 500) + (30 + 40 + 50) + (3 + 4 + 5)) = 2664
Most Upvoted Answer
What is the sum of all three-digit numbers that can be formed using al...
The sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition:
To find the sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition, we need to consider all possible combinations of these digits.
Identifying the Possible Combinations:
The three-digit numbers that can be formed using these digits are:
1. 345
2. 354
3. 435
4. 453
5. 534
6. 543
Calculating the Sum:
To calculate the sum of these numbers, we can add them digit by digit.
First, let's add the hundreds place digit (3) in each number:
3 + 3 + 4 + 4 + 5 + 5 = 24
Next, let's add the tens place digit (4) in each number:
4 + 4 + 3 + 5 + 3 + 5 = 24
Finally, let's add the ones place digit (5) in each number:
5 + 5 + 5 + 3 + 4 + 4 = 26
Now, let's add up the sums of each place:
24 + 24 + 26 = 74
So, the sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition is 74.
However, none of the provided answer options match this sum. Therefore, the given correct answer option 'A' (2664) seems to be incorrect.
It is possible that there may be an error in the provided answer options, as the calculated sum does not match any of them.
To find the sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition, we need to consider all possible combinations of these digits.
Identifying the Possible Combinations:
The three-digit numbers that can be formed using these digits are:
1. 345
2. 354
3. 435
4. 453
5. 534
6. 543
Calculating the Sum:
To calculate the sum of these numbers, we can add them digit by digit.
First, let's add the hundreds place digit (3) in each number:
3 + 3 + 4 + 4 + 5 + 5 = 24
Next, let's add the tens place digit (4) in each number:
4 + 4 + 3 + 5 + 3 + 5 = 24
Finally, let's add the ones place digit (5) in each number:
5 + 5 + 5 + 3 + 4 + 4 = 26
Now, let's add up the sums of each place:
24 + 24 + 26 = 74
So, the sum of all three-digit numbers that can be formed using the digits 3, 4, and 5 without repetition is 74.
However, none of the provided answer options match this sum. Therefore, the given correct answer option 'A' (2664) seems to be incorrect.
It is possible that there may be an error in the provided answer options, as the calculated sum does not match any of them.
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What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?a)2664b)3882c)4044d)4444Correct answer is option 'A'. Can you explain this answer?
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