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…
Question Number 26555 by das47955@mail.com last updated on 26/Dec/17 $$\left(\mathrm{2}\right)\:\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\mathrm{10}\boldsymbol{\mathrm{th}}\:\boldsymbol{\mathrm{trem}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}}\:\left(\mathrm{2}\boldsymbol{\mathrm{x}}−\frac{\boldsymbol{\mathrm{y}}}{\mathrm{2}}\right) \\ $$ Commented by Rasheed.Sindhi last updated on 27/Dec/17 $$\left(\mathrm{2}\boldsymbol{\mathrm{x}}−\frac{\boldsymbol{\mathrm{y}}}{\mathrm{2}}\right)^{?} \\ $$ Terms…
Question Number 26477 by NECx last updated on 26/Dec/17 $${A}\:{number}\:{of}\:{four}\:{different} \\ $$$${digits}\:{is}\:{formed}\:{by}\:{using}\:{the}\: \\ $$$${digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},{in}\:{all}\:{possible} \\ $$$${ways}\:{each}\:{digit}\:{occuring}\:{once} \\ $$$${only}.{find}\:{how}\:{many}\:{of}\:{them}\:{are} \\ $$$${greater}\:{than}\:\mathrm{3400} \\ $$ Answered by mrW1…
Question Number 26480 by NECx last updated on 26/Dec/17 $${Find}\:{the}\:{number}\:{of}\:{all}\:{possible} \\ $$$${different}\:{words}\:{into}\:{which}\:{the} \\ $$$${word}\:{INTERFERE}\:{can}\:{be}\: \\ $$$${converted}\:{by}\:{change}\:{of}\:{place}\:{of}\: \\ $$$${letters},{if}\:{no}\:{two}\:{consonants} \\ $$$${must}\:{be}\:{together}. \\ $$ Answered by mrW1…
Question Number 26473 by NECx last updated on 25/Dec/17 $${How}\:{many}\:{numbers}\:{less}\:{than} \\ $$$$\mathrm{1000}\:{and}\:{divisible}\:{by}\:\mathrm{5}\:{can}\:{be} \\ $$$${formed}\:{with}\:{the}\:{digits}\:\mathrm{0},\:\mathrm{1},\:\mathrm{2}\:,\mathrm{3}\:,\mathrm{4}\:,\mathrm{5}\: \\ $$$$\mathrm{6}\:,\mathrm{7}\:,\mathrm{8}\:,\mathrm{9},{each}\:{digit}\:{not}\:{occuring} \\ $$$${more}\:{than}\:{once}\:{in}\:{each}\:{number}? \\ $$ Answered by mrW1 last updated…
Question Number 157126 by malwan last updated on 20/Oct/21 $${how}\:{many}\:{ways}\:{can}\:{you} \\ $$$${exchange}\:\mathrm{1}\:{dollar}\:{using} \\ $$$$\left(\mathrm{1},\mathrm{5},\mathrm{10},\mathrm{25},\mathrm{50}\right)\:{cents} \\ $$$${example} \\ $$$$\mathrm{1}\:{dollar}\left(\mathrm{100}\:{cents}\right)=\mathrm{2}×\mathrm{50}{cents} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{2}×\mathrm{25}=\mathrm{4}×\mathrm{25} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{1}×\mathrm{25}+\mathrm{1}×\mathrm{10}+\mathrm{1}×\mathrm{5}+\mathrm{10}×\mathrm{1} \\ $$$${and}\:{so}\:{on} \\…