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Factorial Madness

Source: 2019 AMC 10B #14

February 14, 2019
factorial2019 AMC2019 AMC 10BAMC 10AMC

Problem Statement

The base-ten representation for 19!19! is 121,6T5,100,40M,832,H00121,6T5,100,40M,832,H00, where TT, MM, and HH denote digits that are not given. What is T+M+HT+M+H?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>14<spanclass=′latex−bold′>(E)</span>17<span class='latex-bold'>(A) </span>3 \qquad<span class='latex-bold'>(B) </span>8 \qquad<span class='latex-bold'>(C) </span>12 \qquad<span class='latex-bold'>(D) </span>14 \qquad<span class='latex-bold'>(E) </span> 17
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