-
A five digit number is formed using the digits 1,3,5,7 and 9 without repeating any of them. What is the sum of all such possible five digit numbers?
-
- 6666660
- 6666600
- 6666666
- 6666606
Correct Option: B
The digit in unit place is selected in 4! Ways
The digit in tens place is selected in 4! Ways
The digit in hundreds place is selected in 4! Ways
The digit in thousands place is selected in 4! Ways
The digit in ten thousands place is selected in 4! Ways
Sum of all values for 1
4! × 1 × (100 + 101 + 102 + 103 +104) = 4! × 11111 × 1
Similarly for ‘3’ 4! × (11111) × 3
Similarly for ‘5’ 4! × (11111) × 5
Similarly for ‘7’ 4! × (11111) × 7
Similarly for ‘9’ 4! × (11111) × 9
∴ sum of all such numbers
4! × (11111)× (1+ 3 + 5 + 7 + 9)
= 24 × (11111) × 25
= 6666600
