MathDB
8-digit number with only two are same

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April 28, 2009

Problem Statement

How many 8-digit numbers are there such that exactly 7 digits are all different?
<spanclass=′latex−bold′>(A)</span> (93)2⋅6!⋅3<spanclass=′latex−bold′>(B)</span> (83)2⋅7!<spanclass=′latex−bold′>(C)</span> (83)2⋅7!⋅3<spanclass=′latex−bold′>(D)</span> (73)2⋅7!<spanclass=′latex−bold′>(E)</span> (94)2⋅6!⋅8<span class='latex-bold'>(A)</span>\ {{9}\choose{3}}^2 \cdot 6! \cdot 3 \qquad<span class='latex-bold'>(B)</span>\ {{8}\choose{3}}^2 \cdot 7! \qquad<span class='latex-bold'>(C)</span>\ {{8}\choose{3}}^2 \cdot 7! \cdot 3 \\ \qquad<span class='latex-bold'>(D)</span>\ {{7}\choose{3}}^2 \cdot 7! \qquad<span class='latex-bold'>(E)</span>\ {{9}\choose{4}}^2 \cdot 6! \cdot 8
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