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Question Number 110524 by Aina Samuel Temidayo last updated on 29/Aug/20
$$\mathrm{A}\:\mathrm{blind}\:\mathrm{man}\:\mathrm{is}\:\mathrm{to}\:\mathrm{place}\:\mathrm{6}\:\mathrm{letters}\:\mathrm{into}\:\mathrm{6} \\ $$$$\mathrm{pigeon}\:\mathrm{holes},\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can} \\ $$$$\mathrm{atleast}\:\mathrm{5}\:\mathrm{letters}\:\mathrm{be}\:\mathrm{wrongly}\:\mathrm{placed}? \\ $$$$\left(\mathrm{Note}\:\mathrm{that}\:\mathrm{only}\:\mathrm{one}\:\mathrm{letter}\:\mathrm{must}\:\mathrm{be}\:\mathrm{in}\:\mathrm{a}\right. \\ $$$$\left.\mathrm{pigeon}\:\mathrm{hole}\right). \\ $$
Answered by mr W last updated on 30/Aug/20
$${five}\:{letters}\:{wrong}: \\ $$$$\mathrm{6}×\mathrm{44}=\mathrm{264} \\ $$
Commented by Aina Samuel Temidayo last updated on 30/Aug/20
$$\mathrm{This}\:\mathrm{is}\:\mathrm{not}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{options}. \\ $$
Commented by mr W last updated on 30/Aug/20
$${one}\:{letter}\:{right}\:{and}\:{five}\:{letters}\:{wrong}: \\ $$$$\mathrm{6}×!\mathrm{5}=\mathrm{6}×\mathrm{44}=\mathrm{264} \\ $$$${all}\:{six}\:{letters}\:{wrong}: \\ $$$$!\mathrm{6}=\mathrm{265} \\ $$$$\Rightarrow{totally}\:\mathrm{264}+\mathrm{265}=\mathrm{529} \\ $$
Commented by Aina Samuel Temidayo last updated on 30/Aug/20
$$\mathrm{Thanks}. \\ $$