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Question Number 56743 by Tawa1 last updated on 22/Mar/19 Answered by mr W last updated on 23/Mar/19 $$\left(\mathrm{14}\right) \\ $$$${all}\:{possibilities}:\:{C}_{\mathrm{5}} ^{\mathrm{50}} \\ $$$${without}\:{teacher}:\:{C}_{\mathrm{5}} ^{\mathrm{45}} \\…
Question Number 122250 by mr W last updated on 15/Nov/20 Answered by mr W last updated on 15/Nov/20 $${using}\:{generating}\:{function}\:{method} \\ $$$${the}\:{number}\:{of}\:{ways}\:{is}\:{the}\:{coefficient} \\ $$$${of}\:{term}\:{x}^{\mathrm{10}} \:{in}\:{the}\:{expansion} \\…
Question Number 56688 by pieroo last updated on 21/Mar/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{odd}\:\mathrm{numbers},\:\mathrm{greater}\:\mathrm{than} \\ $$$$\mathrm{60000},\:\mathrm{can}\:\mathrm{be}\:\mathrm{made}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digits} \\ $$$$\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{0},\:\mathrm{if}\:\mathrm{no}\:\mathrm{number}\:\mathrm{contains}\:\mathrm{any} \\ $$$$\mathrm{digit}\:\mathrm{more}\:\mathrm{than}\:\mathrm{ones}? \\ $$ Answered by mr W last updated on…
Question Number 56678 by pieroo last updated on 21/Mar/19 $$\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{9}\:\mathrm{whites},\:\mathrm{7}\:\mathrm{red}\:\mathrm{and}\:\mathrm{4}\:\mathrm{blue} \\ $$$$\mathrm{balls}.\:\mathrm{Three}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{picked}\:\mathrm{at}\:\mathrm{random}, \\ $$$$\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\:\mathrm{without}\:\mathrm{replacement}. \\ $$$$\left.\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}: \\ $$$$\mathrm{i}.\:\mathrm{they}\:\mathrm{are}\:\mathrm{all}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color} \\ $$$$\mathrm{ii}.\:\mathrm{there}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{each}\:\mathrm{colour} \\ $$$$\mathrm{iii}.\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{red} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{first}\:\mathrm{one}\:\mathrm{picked} \\…
Question Number 56624 by pieroo last updated on 19/Mar/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2000} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}? \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{will}\:\mathrm{be}\:\mathrm{even}? \\ $$$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}. \\ $$ Commented by pieroo last updated on 19/Mar/19…
Question Number 56615 by pieroo last updated on 19/Mar/19 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{OKINKWO}\:\mathrm{be}\:\mathrm{arranged}?\: \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{arrangements} \\ $$$$\mathrm{does}\:\mathrm{an}\:\mathrm{O}\:\mathrm{occupy}\:\mathrm{both}\:\mathrm{end}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{word}? \\ $$ Commented by mr W last…
Question Number 121851 by bemath last updated on 12/Nov/20 $${How}\:{many}\:{ways}\:{to}\:{arrange}\:{letters}\: \\ $$$${using}\:{letters}\:{in}\:{the}\:{word}\:{OKINKO} \\ $$$$\left({a}\right)\:\mathrm{1260}\:\:\:\:\:\left({b}\right)\:\mathrm{1160}\:\:\:\:\left({c}\right)\:\mathrm{980} \\ $$$$\left({d}\right)\:\mathrm{880}\:\:\:\:\:\:\:\:\left({e}\right)\:\mathrm{720} \\ $$ Commented by liberty last updated on 12/Nov/20…
Question Number 121829 by bemath last updated on 12/Nov/20 Answered by mr W last updated on 12/Nov/20 $${no}\:{empty}:\:\mathrm{3}!=\mathrm{6} \\ $$$${one}\:{empty}:\:\mathrm{3}×\mathrm{2}×\mathrm{3}=\mathrm{18} \\ $$$$\Rightarrow{totally}\:\mathrm{24} \\ $$ Commented…
Question Number 56212 by pieroo last updated on 12/Mar/19 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls} \\ $$$$\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{a}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{restrictions} \\ $$$$\mathrm{b}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{stand}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 12/Mar/19…