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- A five-digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them.
Question 1:
A five-digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers? A. 6666600
Feedback If we fix 1 at the unit’s place, the other digits can be arranged in 4! = 24 ways.
So, there are 24 numbers which have 1 at the unit’s place and sum of these numbers is 24.
Similarly, there will be 24 numbers each with 3, 5, 7 and 9 at the unit’s place.
So, the sum of all the numbers at the unit’s place will be:
24 + 24 × 3 + 24 × 5 + 24 × 7 + 24 × 9 = 24 + 72 + 120 + 168 + 216 = 600.
Similarly, the sum of the digits at the ten’s place, hundred’s place,
thousand’s place and ten thousand’s place will be 600.
So, the sum of all numbers = 600 (1 + 10 +100 +1,000 +10,000) = 6666600.
So, there are 24 numbers which have 1 at the unit’s place and sum of these numbers is 24.
Similarly, there will be 24 numbers each with 3, 5, 7 and 9 at the unit’s place.
So, the sum of all the numbers at the unit’s place will be:
24 + 24 × 3 + 24 × 5 + 24 × 7 + 24 × 9 = 24 + 72 + 120 + 168 + 216 = 600.
Similarly, the sum of the digits at the ten’s place, hundred’s place,
thousand’s place and ten thousand’s place will be 600.
So, the sum of all numbers = 600 (1 + 10 +100 +1,000 +10,000) = 6666600.
B. 6666660
C. 6666666
D. None of these
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