Question:
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 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?
Show Hint
Find how many times each digit appears in each place.
Updated On: Nov 5, 2026
- 6666600
- 6666660
- 6666666
- None
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Count the numbers:
There are \(5! = 120\) numbers.
Step 2: Digit in a given place:
Each digit appears in each place \(4! = 24\) times.
Step 3: Sum:
Sum of the digits \(= 1 + 3 + 5 + 7 + 9 = 25\). The sum of the digits in each place over all numbers is \(24 \times 25 = 600\). Total \(= 600 \times (10000 + 1000 + 100 + 10 + 1) = 600 \times 11111 = 6666600\).
Final Answer:
The correct option is (1): 6666600.
There are \(5! = 120\) numbers.
Step 2: Digit in a given place:
Each digit appears in each place \(4! = 24\) times.
Step 3: Sum:
Sum of the digits \(= 1 + 3 + 5 + 7 + 9 = 25\). The sum of the digits in each place over all numbers is \(24 \times 25 = 600\). Total \(= 600 \times (10000 + 1000 + 100 + 10 + 1) = 600 \times 11111 = 6666600\).
Final Answer:
The correct option is (1): 6666600.
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