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What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]?
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What will be the sum of adding all the possible four digit number form...
Introduction:
To find the sum of all possible four-digit numbers formed by the digits 7, 9, 1, and 3, we need to consider all the permutations of these digits and then calculate their sum. Since we are using each digit only once, there will be a total of 4! (4 factorial) permutations.
Permutations:
The 4! permutations of the digits 7, 9, 1, and 3 are as follows:
- 1793
- 1937
- 1397
- 1379
- 7139
- 7193
- 9173
- 9137
- 3917
- 3971
- 1739
- 1793
- 9317
- 9371
- 7319
- 7391
- 3179
- 3197
- 9173
- 9137
- 3719
- 3791
- 7193
- 7139
Calculating the Sum:
To find the sum of these numbers, we can add the digits in each place value (thousands, hundreds, tens, and units) separately.
Thousands Place:
The sum of the digits in the thousands place will be the sum of the digits 1, 3, 7, and 9 times the number of permutations that have the same digit in the thousands place. Since each digit occurs six times in the units place, we have four groups of six numbers each.
Sum of digits in thousands place = (1+3+7+9) x 6 x 4 = 20 x 6 x 4 = 480
Hundreds Place:
Similarly, the sum of the digits in the hundreds place will also be the sum of the digits 1, 3, 7, and 9 times the number of permutations that have the same digit in the hundreds place.
Sum of digits in hundreds place = (1+3+7+9) x 6 x 4 = 20 x 6 x 4 = 480
Tens Place:
The sum of the digits in the tens place will also be the sum of the digits 1, 3, 7, and 9 times the number of permutations that have the same digit in the tens place.
Sum of digits in tens place = (1+3+7+9) x 6 x 4 = 20 x 6 x 4 = 480
Units Place:
Since each digit occurs six times in the units place, the sum of the digits in the units place will be the sum of all the digits 1, 3, 7, and 9 multiplied by the number of times each digit occurs.
Sum of digits in units place = (1+3+7+9) x 6 = 20 x 6 = 120
Total Sum:
Finally, we can find the total sum by adding the sums of the digits in each place value.
Total Sum = Sum of digits in thousands place + Sum of digits in hundreds place + Sum of digits in tens place + Sum of digits in units place
= 480 + 480 + 480 + 120
To find the sum of all possible four-digit numbers formed by the digits 7, 9, 1, and 3, we need to consider all the permutations of these digits and then calculate their sum. Since we are using each digit only once, there will be a total of 4! (4 factorial) permutations.
Permutations:
The 4! permutations of the digits 7, 9, 1, and 3 are as follows:
- 1793
- 1937
- 1397
- 1379
- 7139
- 7193
- 9173
- 9137
- 3917
- 3971
- 1739
- 1793
- 9317
- 9371
- 7319
- 7391
- 3179
- 3197
- 9173
- 9137
- 3719
- 3791
- 7193
- 7139
Calculating the Sum:
To find the sum of these numbers, we can add the digits in each place value (thousands, hundreds, tens, and units) separately.
Thousands Place:
The sum of the digits in the thousands place will be the sum of the digits 1, 3, 7, and 9 times the number of permutations that have the same digit in the thousands place. Since each digit occurs six times in the units place, we have four groups of six numbers each.
Sum of digits in thousands place = (1+3+7+9) x 6 x 4 = 20 x 6 x 4 = 480
Hundreds Place:
Similarly, the sum of the digits in the hundreds place will also be the sum of the digits 1, 3, 7, and 9 times the number of permutations that have the same digit in the hundreds place.
Sum of digits in hundreds place = (1+3+7+9) x 6 x 4 = 20 x 6 x 4 = 480
Tens Place:
The sum of the digits in the tens place will also be the sum of the digits 1, 3, 7, and 9 times the number of permutations that have the same digit in the tens place.
Sum of digits in tens place = (1+3+7+9) x 6 x 4 = 20 x 6 x 4 = 480
Units Place:
Since each digit occurs six times in the units place, the sum of the digits in the units place will be the sum of all the digits 1, 3, 7, and 9 multiplied by the number of times each digit occurs.
Sum of digits in units place = (1+3+7+9) x 6 = 20 x 6 = 120
Total Sum:
Finally, we can find the total sum by adding the sums of the digits in each place value.
Total Sum = Sum of digits in thousands place + Sum of digits in hundreds place + Sum of digits in tens place + Sum of digits in units place
= 480 + 480 + 480 + 120
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What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]?
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What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]?.
What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the sum of adding all the possible four digit number formed by 7,9,1,3 using each of the digits only once? [Hint : Each of the given digits will occur six times in the units place and there will be 4 groups of 6 number each.]?.
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