CAT 1993 — QA Question 26
Numbers (P&C)Easy
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?
Answer & solution
Correct answer: 6666600
6666600
- B
6666660
- C
6666666
- D
None
Solution
If we assume that any digit is in a fixed position, then the remaining four digits can be arranged in 4! = 24 ways. So each of the 5 digits will appear in each of the five places 24 times. So the sum of the digits in each position is 24(1 + 3 + 5 + 7 + 9) = 600.
Hence, the sum of all such numbers will be 600(1 + 10 + 100 + 1000 + 10000) = 6666600.
Hence, option (a).