2016 AMC 8 Problem 17
Attempt Problem 17 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
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?
Answer: D
Small hint:
First count all four-digit passwords when leading zeroes are allowed.
Big hint:
Then subtract the passwords whose first three digits are forced to be .
Video solution:
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Written solution:
The total number of passwords with no conditions is The condition removes possible passwords since the first are determined, and the last one can be anything. Therefore, the number of acceptable passwords is
Thus, D is the correct answer.
Problem 17 in other years
- 1985 AMC 8
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