Combinatorics: Magic Account Numbers
XAT 2011 · Quantitative Ability & Data Interpretation · Medium · Permutations & Combinations
In 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 . An account number is considered to be a 'magic' number if is exactly the same as or or both. 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?
- A.
9989
- B.
19980
- C.
19989
- D.
19999
- E.
19990
C
Explanation
Case 1: . Total , minus invalid '0000000' gives 9999. Case 2: . Total . Intersection: and . Total overlap . Total .
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