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Category: Permutation and Combination

In-how-many-ways-can-you-go-up-a-staircase-with-20-steps-if-you-take-one-two-or-three-steps-at-a-time-

Question Number 166770 by mr W last updated on 27/Feb/22 $${In}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{go}\:{up}\:{a}\: \\ $$$${staircase}\:{with}\:\mathrm{20}\:{steps}\:{if}\:{you}\:{take}\: \\ $$$${one},\:{two}\:{or}\:{three}\:{steps}\:{at}\:{a}\:{time}? \\ $$ Commented by MJS_new last updated on 27/Feb/22 $$\mathrm{is}\:\mathrm{it}\:\mathrm{121415}?…

A-panel-of-3-women-and-4-men-is-to-be-formed-from-8-women-and-7-men-Find-the-number-of-ways-which-the-panel-can-be-formed-if-it-must-contain-at-least-2-women-

Question Number 35640 by NECx last updated on 21/May/18 $${A}\:{panel}\:{of}\:\mathrm{3}\:{women}\:{and}\:\mathrm{4}\:{men}\:{is} \\ $$$${to}\:{be}\:{formed}\:{from}\:\mathrm{8}\:{women}\:{and} \\ $$$$\mathrm{7}\:{men}.{Find}\:{the}\:{number}\:{of}\:{ways} \\ $$$${which}\:{the}\:{panel}\:{can}\:{be}\:{formed}\:{if} \\ $$$${it}\:{must}\:{contain}\:{at}\:{least}\:\mathrm{2}\:{women}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…

Three-boys-two-girls-and-a-puppy-sit-at-a-round-table-In-how-many-ways-can-they-be-arranged-if-the-puppy-is-to-be-seated-i-between-the-two-girls-ii-between-any-two-boys-

Question Number 35639 by NECx last updated on 21/May/18 $${Three}\:{boys},{two}\:{girls}\:{and}\:{a}\:{puppy} \\ $$$${sit}\:{at}\:{a}\:{round}\:{table}.{In}\:{how}\:{many} \\ $$$${ways}\:{can}\:{they}\:{be}\:{arranged}\:{if}\:{the} \\ $$$${puppy}\:{is}\:{to}\:{be}\:{seated} \\ $$$$\left.{i}\right){between}\:{the}\:{two}\:{girls} \\ $$$$\left.{ii}\right){between}\:{any}\:{two}\:{boys} \\ $$ Commented by NECx…

A-woman-sent-8-letters-to-her-friends-The-letters-are-kept-in-the-addressed-envelopes-at-random-The-probability-that-4-friends-receive-correct-letters-and-4-letters-go-to-wrong-destination-is-

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…

In-how-many-ways-can-a-committee-of-11-people-be-selected-from-9-people-

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-35151

Question Number 35151 by Victor31926 last updated on 16/May/18 Answered by Rasheed.Sindhi last updated on 16/May/18 $$\because\mathrm{5}\mid\mathrm{5}!\:\&\:\mathrm{5}!\:\mid\:\mathrm{50}!,\mathrm{40}!,\mathrm{30}!,\mathrm{20}!,\mathrm{10}! \\ $$$$\therefore\:\mathrm{5}\mid\:\mathrm{50}!,\mathrm{40}!,\mathrm{30}!,\mathrm{20}!,\mathrm{10}! \\ $$$$\:\therefore\mathrm{5}\mid\:\left(\mathrm{50}!+\mathrm{40}!+\mathrm{30}!+\mathrm{20}!+\mathrm{10}!\right) \\ $$$$\therefore\:\mathrm{The}\:\mathrm{remainder}=\mathrm{0} \\ $$…