Question Number 159715 by cortano last updated on 20/Nov/21 Commented by mr W last updated on 20/Nov/21 $${if}\:{one}\:{draws}\:\mathrm{12}\:{balls},\:{they}\:{could}\:{be} \\ $$$$\mathrm{3}\:{red}\:{ones},\:\mathrm{3}\:{green}\:{ones},\:\mathrm{3}\:{blacks}, \\ $$$$\mathrm{3}\:{blue}\:{one}.\:{if}\:{one}\:{draws}\:{one}\:{ball}\:{more}, \\ $$$${one}\:{color}\:{must}\:{have}\:\mathrm{4}\:{balls}.\:{so}\:{the} \\…
Question Number 93764 by DuDono last updated on 14/May/20 $$\mathrm{define} \\ $$$$\underset{{x}=\mathrm{0}} {\overset{{k}} {\sum}}\frac{{n}!}{{x}!\left({n}−{x}\right)!} \\ $$$$\mathrm{without}\:\Sigma\:\mathrm{symbol} \\ $$ Commented by mr W last updated on…
Question Number 159259 by pticantor last updated on 14/Nov/21 $$\boldsymbol{{montre}}\:\boldsymbol{{que}}\: \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{C}}_{\mathrm{2}\boldsymbol{{n}}} ^{\mathrm{2}\boldsymbol{{k}}} =\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} \\ $$ Answered by mr W last updated on…
Question Number 28015 by ajfour last updated on 18/Jan/18 Commented by ajfour last updated on 18/Jan/18 $${Q}.\mathrm{27997}\:{solution} \\ $$ Answered by ajfour last updated on…
Question Number 93450 by john santu last updated on 13/May/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{x}^{\mathrm{9}} \:\mathrm{in}\:\mathrm{expansion}\:\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)×…×\left(\mathrm{1}+\mathrm{x}^{\mathrm{100}} \right)\:? \\ $$ Answered by john…
Question Number 158955 by mr W last updated on 11/Nov/21 Answered by mr W last updated on 15/Nov/21 $${let}'{s}\:{look}\:{at}\:{the}\:{general}\:{case}\:{with}\:{n} \\ $$$${students}\:{into}\:{r}\:{schools}.\:{both}\:{students} \\ $$$$\left({objects}\right)\:{and}\:{schools}\:\left({boxes}\right)\:{are} \\ $$$${distinct}.…
Question Number 27514 by NECx last updated on 08/Jan/18 $${The}\:{president}\:{of}\:{a}\:{republic}\:{wishes} \\ $$$${to}\:{assign}\:{the}\:{premiership},{the}\: \\ $$$${vice}-{premiership},{and}\:{six}\:{other} \\ $$$${cabinet}\:{posts}\:{to}\:{a}\:{selected}\:{group} \\ $$$${of}\:\mathrm{8},{comprising}\:{of}\:\mathrm{6}\:{career} \\ $$$${diplomats}\:{and}\:\mathrm{2}\:{business}\:{men}.{If} \\ $$$${none}\:{of}\:{the}\:{business}\:{men}\:{can}\:{be} \\ $$$${made}\:{premier}\:{or}\:{vice}\:{premier},{in} \\…
Question Number 27513 by NECx last updated on 08/Jan/18 $${Using}\:{only}\:{the}\:{integers}\:\mathrm{4}\:{to}\:\mathrm{8}, \\ $$$${how}\:{many}\:{even}\:{numbers}\:{can}\:{be} \\ $$$${formed}\:{if}\:{each}\:{must}\:{lie}\:{between} \\ $$$$\mathrm{4000}\:{and}\:\:\mathrm{9000}? \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 158529 by mr W last updated on 11/Nov/21 $${In}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{30}\:{students} \\ $$$${be}\:{distributed}\:{to}\:\mathrm{10}\:{schools},\:{if} \\ $$$$\mathrm{1}.\:{each}\:{school}\:{should}\:{get}\:{at}\:{least}\:{one} \\ $$$$\:\:\:\:\:{student}. \\ $$$$\mathrm{2}.\:{no}\:{restriction} \\ $$ Answered by cortano last…
Question Number 92923 by Ar Brandon last updated on 09/May/20 $$\mathrm{Solve} \\ $$$$\mathrm{1}+\frac{\mathrm{x}}{\mathrm{2}!}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{4}!}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}!}+\centerdot\centerdot\centerdot\:=\mathrm{0} \\ $$ Answered by mr W last updated on 09/May/20…