Question Number 104155 by mr W last updated on 19/Jul/20 Commented by mr W last updated on 19/Jul/20 $${an}\:{unsolved}\:{old}\:{question} \\ $$ Commented by mr W…
Question Number 104134 by bemath last updated on 19/Jul/20 $${what}\:{is}\:{the}\:{coefficient}\:{x}^{\mathrm{15}} \\ $$$${in}\:{the}\:{expansion}\:{of}\:{x}^{\mathrm{6}} \left(\mathrm{1}−{x}\right)^{\mathrm{11}} \\ $$ Answered by bobhans last updated on 19/Jul/20 $$''\boldsymbol{{x}}^{\mathrm{6}} \left(\mathrm{1}−\boldsymbol{{x}}\right)^{\mathrm{11}} \:=\:\boldsymbol{{x}}^{\mathrm{6}}…
Question Number 103903 by mr W last updated on 18/Jul/20 $${a}\:\mathrm{100}\:{cm}\:{long}\:{rod}\:{should}\:{be}\:{divided} \\ $$$${into}\:\mathrm{3}\:{parts}.\:{the}\:{length}\:{of}\:{each}\:{part} \\ $$$${in}\:{cm}\:{should}\:{be}\:{integer}.\:{in}\:{how}\: \\ $$$${many}\:{different}\:{ways}\:{can}\:{this}\:{be} \\ $$$${done}? \\ $$ Commented by bobhans last…
Question Number 103826 by bobhans last updated on 17/Jul/20 $${In}\:{the}\:{expansion}\:{of}\:\left(\mathrm{1}+{x}\right)^{\mathrm{20}} \:{if}\:{the} \\ $$$${coefficient}\:{of}\:{x}^{{r}} \:{is}\:{twice}\:{the}\:{coefficient} \\ $$$${of}\:{x}^{{r}−\mathrm{1}} ,\:{what}\:{the}\:{value}\:{of}\:{the} \\ $$$${coefficient}?\: \\ $$ Answered by bramlex last…
Question Number 103716 by mr W last updated on 16/Jul/20 Commented by mr W last updated on 16/Jul/20 $${after}\:{thinking}\:{about}\:{it}\:{for}\:{two}\:{days}, \\ $$$${i}\:{think}\:{i}\:{have}\:{found}\:{the}\:{general} \\ $$$${solution}\:{which}\:{is}\:{simply} \\ $$$$\boldsymbol{{C}}_{\boldsymbol{{m}}}…
Question Number 169159 by SLVR last updated on 25/Apr/22 $${The}\:{remainder}\:{of} \\ $$$$\mathrm{13}^{\mathrm{13}} {when}\: \\ $$$${divided}\:{by}\:\mathrm{99}\:{is} \\ $$ Commented by SLVR last updated on 25/Apr/22 $${kindly}\:{solve}..…
Question Number 103606 by bemath last updated on 16/Jul/20 $${an}\:{integer}\:{n}\:{between}\:\mathrm{1}\:{and}\:\mathrm{98}\:, \\ $$$${inclusive}\:{is}\:{to}\:{be}\:{chosen}\:{at} \\ $$$${random}.\:{what}\:{is}\:{the}\:{probability} \\ $$$${that}\:{n}\left({n}+\mathrm{1}\right)\:{will}\:{be}\:{divisible}\:{by}\:\mathrm{3} \\ $$ Commented by bemath last updated on 16/Jul/20…
Question Number 103513 by bemath last updated on 15/Jul/20 $${coefficient}\:{of}\:{x}^{\mathrm{5}} \:{in}\:{expansion} \\ $$$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{5}} \left(\mathrm{1}+{x}\right)^{\mathrm{4}} \:{equal}\:{to}\: \\ $$$$\left({a}\right)\:\mathrm{40}\:\:\:\:\:\:\left({b}\right)\:\mathrm{45}\:\:\:\:\:\left({c}\right)\:\mathrm{50}\:\:\:\:\left({d}\right)\:\mathrm{55} \\ $$$$\left({e}\right)\:\mathrm{60} \\ $$ Answered by OlafThorendsen…
Question Number 103410 by Ar Brandon last updated on 14/Jul/20 $$\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{k}!}=? \\ $$ Answered by mathmax by abdo last updated on 15/Jul/20…
Question Number 103406 by mr W last updated on 16/Jul/20 $$\mathrm{100}\:{students}\:{are}\:{standing}\:{in}\:{a}\:{row}. \\ $$$$\mathrm{4}\:{students}\:{should}\:{be}\:{selected}\:{in}\:{the} \\ $$$${way}\:{that}\:{no}\:{two}\:{of}\:{them}\:{are}\:{next}\:{to} \\ $$$${each}\:{other}.\:{how}\:{many}\:{ways}\:{do}\:{you} \\ $$$${have}\:{to}\:{do}\:{this}? \\ $$ Commented by bobhans last…