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…
Question Number 27270 by das47955@mail.com last updated on 05/Jan/18 $$\left(\mathrm{1}\right)\:\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{are}}\:\mathrm{20}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{and}}\:\mathrm{10}\:\boldsymbol{\mathrm{girls}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{class}}.\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{committee}}\:\boldsymbol{\mathrm{of}}\:\mathrm{6}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}} \\ $$$$\boldsymbol{\mathrm{chosen}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{random}}\:\boldsymbol{\mathrm{having}}\:\boldsymbol{\mathrm{atleast}} \\ $$$$\mathrm{2}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{and}}\:\mathrm{2}\:\boldsymbol{\mathrm{girls}},\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{probability}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{ara}}\:\mathrm{3}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{committee}} \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{are}}\:\mathrm{4}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\: \\…
Question Number 157980 by zainaltanjung last updated on 30/Oct/21 $$\mathrm{Calculate}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{below} \\ $$$$\left.\:\:\:\:\:\:\:\:\mathrm{a}\right).\:\:\frac{\mathrm{7}!}{\left(\mathrm{5}−\mathrm{1}\right)!}\:=…… \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\mathrm{b}\right).\:\:\frac{\mathrm{5}!×\mathrm{3}!}{\mathrm{4}!}\:=…… \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\right).\:\:\mathrm{6}!\:\mathrm{4}!\:=…\:\:\:\:\:\:\:\: \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}\right).\:\:\frac{\mathrm{7}!}{\mathrm{3}!}×\frac{\mathrm{2}!}{\mathrm{5}!}\:=…… \\ $$ Answered by puissant last updated…
Question Number 92319 by jagoll last updated on 06/May/20 $$\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{2}}\right).\mathrm{log}\:_{\mathrm{3}/\mathrm{4}} \left(\mathrm{x}^{\mathrm{2}} \right)\:\geqslant\: \\ $$$$\mathrm{log}\:_{\mathrm{3}/\mathrm{4}} \left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{2}}\right)\: \\ $$ Commented by john santu last updated on…
Question Number 26732 by math solver last updated on 28/Dec/17 Commented by prakash jain last updated on 28/Dec/17 $$=\:^{\mathrm{5}} {P}_{\mathrm{4}} ×^{\mathrm{3}} {P}_{\mathrm{3}} =\mathrm{5}!×\mathrm{3}!=\mathrm{720} \\ $$…
Question Number 26554 by das47955@mail.com last updated on 26/Dec/17 $$\left(\mathrm{2}\right)\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{middle}}\:\boldsymbol{\mathrm{trem}}\left(\boldsymbol{\mathrm{s}}\right)\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{following}}− \\ $$$$\:\:\:\:\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }\right)^{\mathrm{14}} \\ $$ Answered by prakash jain last updated on…