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Question Number 177007 by Ar Brandon last updated on 29/Sep/22

Answered by mr W last updated on 29/Sep/22

1. he buys the 13^(th)  floor:  12^(th)  floor is also bought. to buy the   rest 6 floors there are C_6 ^(11) =462 ways.  2. he doesn′t buy the 13^(th)  floor:  to buy 8 floors there are  C_8 ^(12) =495 ways.  totally there are 462+495=957 ways  to buy 8 floors.

$$\mathrm{1}.\:{he}\:{buys}\:{the}\:\mathrm{13}^{{th}} \:{floor}: \\ $$$$\mathrm{12}^{{th}} \:{floor}\:{is}\:{also}\:{bought}.\:{to}\:{buy}\:{the}\: \\ $$$${rest}\:\mathrm{6}\:{floors}\:{there}\:{are}\:{C}_{\mathrm{6}} ^{\mathrm{11}} =\mathrm{462}\:{ways}. \\ $$$$\mathrm{2}.\:{he}\:{doesn}'{t}\:{buy}\:{the}\:\mathrm{13}^{{th}} \:{floor}: \\ $$$${to}\:{buy}\:\mathrm{8}\:{floors}\:{there}\:{are} \\ $$$${C}_{\mathrm{8}} ^{\mathrm{12}} =\mathrm{495}\:{ways}. \\ $$$${totally}\:{there}\:{are}\:\mathrm{462}+\mathrm{495}=\mathrm{957}\:{ways} \\ $$$${to}\:{buy}\:\mathrm{8}\:{floors}. \\ $$

Commented by Ar Brandon last updated on 29/Sep/22

Thank you, Sir !

Commented by Tawa11 last updated on 02/Oct/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

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