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Question Number 35151 by Victor31926 last updated on 16/May/18
Answered by Rasheed.Sindhi last updated on 16/May/18
$$\because\mathrm{5}\mid\mathrm{5}!\:\&\:\mathrm{5}!\:\mid\:\mathrm{50}!,\mathrm{40}!,\mathrm{30}!,\mathrm{20}!,\mathrm{10}! \\ $$$$\therefore\:\mathrm{5}\mid\:\mathrm{50}!,\mathrm{40}!,\mathrm{30}!,\mathrm{20}!,\mathrm{10}! \\ $$$$\:\therefore\mathrm{5}\mid\:\left(\mathrm{50}!+\mathrm{40}!+\mathrm{30}!+\mathrm{20}!+\mathrm{10}!\right) \\ $$$$\therefore\:\mathrm{The}\:\mathrm{remainder}=\mathrm{0} \\ $$