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Question Number 100971 by john santu last updated on 29/Jun/20 $$\mathrm{A}\:\mathrm{woman}\:\mathrm{sent}\:\mathrm{8}\:\mathrm{letters}\:\mathrm{to}\:\mathrm{her}\: \\ $$$$\mathrm{friends}.\:\mathrm{The}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{kept}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{addressed}\:\mathrm{envelopes}\:\mathrm{at}\:\mathrm{random}.\: \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{4}\:\mathrm{friends}\: \\ $$$$\mathrm{receive}\:\mathrm{correct}\:\mathrm{letters}\:\mathrm{and}\:\mathrm{4}\:\mathrm{letters}\: \\ $$$$\mathrm{go}\:\mathrm{to}\:\mathrm{wrong}\:\mathrm{destination},\:\mathrm{is}\:\_\_\_\: \\ $$ Answered by…
Question Number 35347 by chakraborty ankit last updated on 18/May/18 Answered by Rasheed.Sindhi last updated on 18/May/18 $$\mathrm{Q}#\mathrm{1}\left(\mathrm{i}\right) \\ $$$$\mathrm{Let}\:\mathrm{P}_{\mathrm{1}} ,\mathrm{P}_{\mathrm{2}} ,\mathrm{P}_{\mathrm{3}} ,\mathrm{P}_{\mathrm{4}} ,\mathrm{P}_{\mathrm{5}} \:\&\:\mathrm{P}_{\mathrm{6}}…
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Question Number 35165 by NECx last updated on 16/May/18 $${In}\:{how}\:{many}\:{ways}\:{can}\:{a}\:{committee} \\ $$$${of}\:\mathrm{11}\:{people}\:{be}\:{selected}\:{from}\:\mathrm{9} \\ $$$${people}. \\ $$ Commented by Rasheed.Sindhi last updated on 16/May/18 $$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{select}\:\mathrm{a}\:\mathrm{committee}\:\mathrm{of}\:\mathrm{11} \\…
Question Number 35151 by Victor31926 last updated on 16/May/18 Answered by Rasheed.Sindhi last updated on 16/May/18 $$\because\mathrm{5}\mid\mathrm{5}!\:\&\:\mathrm{5}!\:\mid\:\mathrm{50}!,\mathrm{40}!,\mathrm{30}!,\mathrm{20}!,\mathrm{10}! \\ $$$$\therefore\:\mathrm{5}\mid\:\mathrm{50}!,\mathrm{40}!,\mathrm{30}!,\mathrm{20}!,\mathrm{10}! \\ $$$$\:\therefore\mathrm{5}\mid\:\left(\mathrm{50}!+\mathrm{40}!+\mathrm{30}!+\mathrm{20}!+\mathrm{10}!\right) \\ $$$$\therefore\:\mathrm{The}\:\mathrm{remainder}=\mathrm{0} \\ $$…
Question Number 34930 by NECx last updated on 13/May/18 $${A}\:{committee}\:{of}\:\mathrm{4}\:{is}\:{to}\:{be}\:{formed} \\ $$$${from}\:\mathrm{4}\:{principals} \\ $$$${and}\:\mathrm{5}\:{students}.{In}\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}\:{if}\:{a}\:{particular} \\ $$$${student}\:{and}\:{a}\:{principal}\:{must}\:{be} \\ $$$${in}\:{the}\:{committee}. \\ $$$$ \\ $$ Commented…
Question Number 100444 by mr W last updated on 26/Jun/20 $${Find}\:{the}\:{number}\:{of}\:{five}−{digit}\:{numbers} \\ $$$${containing}\:{exactly}\:{three}\:{different} \\ $$$${digits}?\:{Examples}:\:\mathrm{12312},\:\mathrm{12224} \\ $$ Answered by Rasheed.Sindhi last updated on 28/Jun/20 $$\:^{\bullet}…
Question Number 34878 by NECx last updated on 12/May/18 $${show}\:{that} \\ $$$$\overset{{n}+{r}−\mathrm{1}} {{C}}_{{n}−\mathrm{1}} =\overset{{n}+{r}−\mathrm{1}} {{C}}_{{r}} \\ $$ Answered by Rasheed.Sindhi last updated on 12/May/18 $$\:^{\mathrm{n}}…