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National and Regional Contests
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MAA AMC
AMC 12/AHSME
2000 AMC 12/AHSME
23
23
Part of
2000 AMC 12/AHSME
Problems
(1)
Professor Gamble
Source:
3/23/2008
Professor Gamble buys a lottery ticket, which requires that he pick six different integers from
1
1
1
through
46
46
46
, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property— the sum of the base-ten logarithms is an integer. What is the probability that Professor Gamble holds the winning ticket?
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1
<span class='latex-bold'>(A)</span>\ 1/5 \qquad <span class='latex-bold'>(B)</span>\ 1/4 \qquad <span class='latex-bold'>(C)</span>\ 1/3 \qquad <span class='latex-bold'>(D)</span>\ 1/2 \qquad <span class='latex-bold'>(E)</span>\ 1
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1/5
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1/4
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1/3
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D
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1/2
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1
logarithms
probability