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…
Question Number 90503 by john santu last updated on 24/Apr/20 Commented by john santu last updated on 24/Apr/20 $${a}\:{total}\:{of}\:\mathrm{20}\:{marble}\: \\ $$ Commented by jagoll last…
Question Number 155842 by zainaltanjung last updated on 05/Oct/21 $$\mathrm{Prof}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\:\mathrm{n}.\mathrm{n}!=\mathrm{11}!−\mathrm{1} \\ $$ Commented by puissant last updated on 05/Oct/21 $${Q}\mathrm{155803} \\…
Question Number 155816 by cortano last updated on 05/Oct/21 $$\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\mathrm{formed} \\ $$$$\:\mathrm{by}\:\mathrm{using}\:\mathrm{all}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6} \\ $$$$\:\mathrm{only}\:\mathrm{once}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{25}. \\ $$ Answered by talminator2856791 last updated on 05/Oct/21 $$\:\mathrm{4}!\:=\:\mathrm{24} \\…