2016 AMC 8 Problems/Problem 17: Difference between revisions
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An ATM password at Fred's Bank is composed of four digits from <math>0</math> to <math>9</math>, with repeated digits allowable. If no password may begin with the sequence <math>9,1,1,</math> then how many passwords are possible? | An ATM password at Fred's Bank is composed of four digits from <math>0</math> to <math>9</math>, with repeated digits allowable. If no password may begin with the sequence <math>9,1,1,</math> then how many passwords are possible? | ||
<math>\textbf{(A)}\mbox{ }30\qquad\textbf{(B)}\mbox{ }7290\qquad\textbf{(C)}\mbox{ }9000\qquad\textbf{(D)}\mbox{ }9990\qquad\textbf{(E)}\mbox{ }9999</math> | <math>\textbf{(A)}\mbox{ }30\qquad\textbf{(B)}\mbox{ }7290\qquad\textbf{(C)}\mbox{ }9000\qquad\textbf{(D)}\mbox{ }9990\qquad\textbf{(E)}\mbox{ }9999</math> | ||
==Solution== | ==Solution== | ||
Revision as of 11:39, 23 November 2016
An ATM password at Fred's Bank is composed of four digits from 
to 
, with repeated digits allowable. If no password may begin with the sequence 
then how many passwords are possible?
Solution
For the first three digits, there are 
combinations since 
is not allowed. For the final digit, any of the 
numbers are allowed. 
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
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