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 $${how}\:{many}\:{ways}\:{can}\:{you} \\ $$$${exchange}\:\mathrm{1}\:{dollar}\:{using} \\ $$$$\left(\mathrm{1},\mathrm{5},\mathrm{10},\mathrm{25},\mathrm{50}\right)\:{cents} \\ $$$${example} \\ $$$$\mathrm{1}\:{dollar}\left(\mathrm{100}\:{cents}\right)=\mathrm{2}×\mathrm{50}{cents} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{2}×\mathrm{25}=\mathrm{4}×\mathrm{25} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{1}×\mathrm{25}+\mathrm{1}×\mathrm{10}+\mathrm{1}×\mathrm{5}+\mathrm{10}×\mathrm{1} \\ $$$${and}\:{so}\:{on} \\…
Question Number 25929 by 786786AM last updated on 16/Dec/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\:\mathrm{coefficients}\:\mathrm{of}\:\mathrm{x}^{\mathrm{m}} \:\mathrm{and}\:\mathrm{x}^{\mathrm{n}} \:\mathrm{in}\:\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{m}+\mathrm{n}} \mathrm{are}\:\mathrm{equal}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 25928 by 786786AM last updated on 16/Dec/17 $$\mathrm{Expand}\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{4}} .\mathrm{H}\boldsymbol{\mathrm{ence}},\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{S}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{S}}=\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{4}} −\mathrm{4}\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{3}} +\mathrm{6}\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{} +\mathrm{1}. \\ $$ Terms of Service Privacy…
Question Number 156979 by cortano last updated on 18/Oct/21 Commented by cortano last updated on 18/Oct/21 $$\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:{C}_{{k}} ^{\:{n}} \:=\mathrm{0}\: \\ $$ Commented…
Question Number 91230 by waseemyaqoobese@gmail.com last updated on 28/Apr/20 $$\underset{{j}={o}} {\overset{{m}} {\sum}}\:\:\overset{{a}} {\:}{C}_{{j}} \:\overset{{b}} {\:}{C}_{{m}−{j}} \:\:=\:\overset{{a}+{b}} {\:}{C}_{{m}} \\ $$$${solve}\:{this}\:{problem} \\ $$ Answered by ~blr237~ last…
Question Number 25314 by ibraheem160 last updated on 08/Dec/17 $${prove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$ Commented by prakash jain last updated on 08/Dec/17 $$\mathrm{please}\:\mathrm{see}\:\mathrm{question}\:\mathrm{25237}. \\ $$ Answered by…
Question Number 25237 by Mr eaay last updated on 06/Dec/17 $${prooove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$ Commented by prakash jain last updated on 07/Dec/17 $$\mathrm{It}\:\mathrm{is}\:\mathrm{a}\:\mathrm{notation}\:\mathrm{simplication} \\ $$$$\mathrm{that}\:\mathrm{defines}\:\mathrm{empty}\:\mathrm{products} \\…
Question Number 90531 by Mikael_786 last updated on 24/Apr/20 $${Please}\:{help}\:{me}\:{to}\:{find}\:{the}\:{value} \\ $$$${of}\:\:\:'{n}' \\ $$$${C}_{\mathrm{8}} ^{{n}+\mathrm{3}} ={C}_{\mathrm{20}} ^{{n}+\mathrm{3}} \\ $$ Commented by mr W last updated…