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Question Number 11855 by tawa last updated on 02/Apr/17
Ten men are present at a club. In how many ways can four be chosen to  play bridge if two men refuse to sit at the same table.
$$\mathrm{Ten}\:\mathrm{men}\:\mathrm{are}\:\mathrm{present}\:\mathrm{at}\:\mathrm{a}\:\mathrm{club}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{four}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{to} \\ $$$$\mathrm{play}\:\mathrm{bridge}\:\mathrm{if}\:\mathrm{two}\:\mathrm{men}\:\mathrm{refuse}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{table}. \\ $$
Answered by sandy_suhendra last updated on 03/Apr/17
let the 2 men are A and B  if A is chosen and B isn′t= 8C3  if B is chosen and A isn′t = 8C3  if A and B aren′t chosen = 8C4  the whole ways=8C3+8C3+8C4                                    =56+56+70=182
$$\mathrm{let}\:\mathrm{the}\:\mathrm{2}\:\mathrm{men}\:\mathrm{are}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{if}\:\mathrm{A}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{and}\:\mathrm{B}\:\mathrm{isn}'\mathrm{t}=\:\mathrm{8C3} \\ $$$$\mathrm{if}\:\mathrm{B}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{and}\:\mathrm{A}\:\mathrm{isn}'\mathrm{t}\:=\:\mathrm{8C3} \\ $$$$\mathrm{if}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{aren}'\mathrm{t}\:\mathrm{chosen}\:=\:\mathrm{8C4} \\ $$$$\mathrm{the}\:\mathrm{whole}\:\mathrm{ways}=\mathrm{8C3}+\mathrm{8C3}+\mathrm{8C4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{56}+\mathrm{56}+\mathrm{70}=\mathrm{182} \\ $$$$ \\ $$
Commented by tawa last updated on 03/Apr/17
God bless you sir.
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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