6. A thief tries to open a door with a code: it has 12 press-buttons labeled 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, #, and expects six digits followed by either # or *. How many codes are possible: (i) with no further indication? (ii) if no number is repeated? By observing the buttons, one can try to guess the frequency of the use of each button. Indeed, thief notices that the buttons 4, 6, 7, 8, * are never used (not in the code), the button 1 appears at least twice, and there is no guarantee for the other digits. (iii) How many codes are possible with this new hint? (iv) How many codes are possible if the thief realizes also that 1 appears strictly more times than 9, which appears strictly more times than 2?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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6. A thief tries to open a door with a code: it has 12 press-buttons labeled 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, #, and expects six digits followed by either # or *. How many codes are possible:
(i) with no further indication?
(ii) if no number is repeated?
By observing the buttons, one can try to guess the frequency of the use of each button. Indeed,
thief notices that the buttons 4, 6, 7, 8, * are never used (not in the code), the button 1 appears at
least twice, and there is no guarantee for the other digits.
(iii) How many codes are possible with this new hint?
(iv) How many codes are possible if the thief realizes also that 1 appears strictly more times than
9, which appears strictly more times than 2?
Transcribed Image Text:6. A thief tries to open a door with a code: it has 12 press-buttons labeled 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, #, and expects six digits followed by either # or *. How many codes are possible: (i) with no further indication? (ii) if no number is repeated? By observing the buttons, one can try to guess the frequency of the use of each button. Indeed, thief notices that the buttons 4, 6, 7, 8, * are never used (not in the code), the button 1 appears at least twice, and there is no guarantee for the other digits. (iii) How many codes are possible with this new hint? (iv) How many codes are possible if the thief realizes also that 1 appears strictly more times than 9, which appears strictly more times than 2?
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