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Question Number 111732 by Aina Samuel Temidayo last updated on 04/Sep/20
$$\mathrm{A}\:\mathrm{blind}\:\mathrm{man}\:\mathrm{is}\:\mathrm{to}\:\mathrm{place}\:\mathrm{5}\:\mathrm{letters}\:\mathrm{into}\:\mathrm{5} \\ $$$$\mathrm{pigeon}\:\mathrm{holes},\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{letters}\:\mathrm{be}\:\mathrm{wrongly}\:\mathrm{placed}? \\ $$$$\left(\mathrm{note}\:\mathrm{that}\:\mathrm{only}\:\mathrm{one}\:\mathrm{letter}\:\mathrm{must}\:\mathrm{be}\:\mathrm{in}\:\mathrm{a}\right. \\ $$$$\left.\mathrm{pigeon}\:\mathrm{hole}\right) \\ $$
Answered by mr W last updated on 04/Sep/20
$${one}\:{letter}\:{is}\:{correct}\:{arranged}: \\ $$$${there}\:{is}\:\mathrm{5}\:{ways} \\ $$$${the}\:{other}\:\mathrm{4}\:{letters}\:{are}\:{disarranged}: \\ $$$${there}\:{are}\:!\mathrm{4}=\mathrm{9}\:{ways} \\ $$$$ \\ $$$$\Rightarrow\mathrm{5}×\mathrm{9}=\mathrm{45}\:{ways} \\ $$
Commented by Aina Samuel Temidayo last updated on 04/Sep/20
$$\mathrm{Thanks}. \\ $$