ln a bank the account numbers are all 8 digit numbers, and they all start with the digit 2. So, an account number can be represented as 2x1x2x3x4x5x6x7. An account number is considered to be a ‘magic’ number if x1x2x3 is exactly the same as x4x5x6, or x5x6x7 or both. xi can take values from 0 to 9, but 2 followed by seven 0s is not a valid account number. What is the maximum possible number of customers having a ‘magic’ account number?
Explanation:
x1x2x3x4x5x6x7 can be of the form abcdabc or abcabcd.
abc can be chosen in 10 × 10 × 10 = 1000 ways.
d can be chosen in 10 ways.
∴ x1x2x3x4x5x6x7 can be chosen in 2 × 1000 × 10 = 20000 ways.
However, this includes the ways in which all of a, b, c and d are 0, 1, 2, 3, …, 9, twice.
We subtract these numbers to get 20000 – 10 = 19990
We also don’t want 2000000.
∴ The total number of ways = 19989.
Hence, option (c).
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.