Question Number 177007 by Ar Brandon last updated on 29/Sep/22
Answered by mr W last updated on 29/Sep/22
$$\mathrm{1}.\:{he}\:{buys}\:{the}\:\mathrm{13}^{{th}} \:{floor}: \\ $$$$\mathrm{12}^{{th}} \:{floor}\:{is}\:{also}\:{bought}.\:{to}\:{buy}\:{the}\: \\ $$$${rest}\:\mathrm{6}\:{floors}\:{there}\:{are}\:{C}_{\mathrm{6}} ^{\mathrm{11}} =\mathrm{462}\:{ways}. \\ $$$$\mathrm{2}.\:{he}\:{doesn}'{t}\:{buy}\:{the}\:\mathrm{13}^{{th}} \:{floor}: \\ $$$${to}\:{buy}\:\mathrm{8}\:{floors}\:{there}\:{are} \\ $$$${C}_{\mathrm{8}} ^{\mathrm{12}} =\mathrm{495}\:{ways}. \\ $$$${totally}\:{there}\:{are}\:\mathrm{462}+\mathrm{495}=\mathrm{957}\:{ways} \\ $$$${to}\:{buy}\:\mathrm{8}\:{floors}. \\ $$
Commented by Ar Brandon last updated on 29/Sep/22
Thank you, Sir !
Commented by Tawa11 last updated on 02/Oct/22
$$\mathrm{Great}\:\mathrm{sir} \\ $$