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Category: Permutation and Combination

Given-a-10-digit-number-X-1345789026-How-many-10-digit-number-that-can-be-made-using-every-digit-from-X-with-condition-If-a-number-n-is-located-in-k-th-position-of-X-then-the-new-created-numb

Question Number 137035 by mr W last updated on 29/Mar/21 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:{X}\:=\:\mathrm{1345789026} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{using}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{from}\:{X},\:\mathrm{with}\:\mathrm{condition}: \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:{n}\:\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{created}\:\mathrm{number}\:\mathrm{must}\:\mathrm{not}\:\mathrm{contain} \\ $$$$\mathrm{number}\:{n}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position} \\ $$$$…

Mr-A-wants-to-deliver-7-letters-to-his-7-friends-so-that-each-gets-1-letter-All-of-the-letters-are-written-of-the-addresses-of-his-7-friends-Find-the-probbility-that-3-of-his-friends-receive-the-co

Question Number 136448 by adhigenz last updated on 22/Mar/21 $$\mathrm{Mr}.\mathrm{A}\:\mathrm{wants}\:\mathrm{to}\:\mathrm{deliver}\:\mathrm{7}\:\mathrm{letters}\:\mathrm{to}\:\mathrm{his}\:\mathrm{7}\:\mathrm{friends}\:\mathrm{so}\:\mathrm{that}\:\mathrm{each}\:\mathrm{gets}\:\mathrm{1}\:\mathrm{letter}. \\ $$$$\mathrm{All}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{written}\:\mathrm{of}\:\mathrm{the}\:\mathrm{addresses}\:\mathrm{of}\:\mathrm{his}\:\mathrm{7}\:\mathrm{friends}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probbility}\:\mathrm{that}, \\ $$$$\mathrm{3}\:\mathrm{of}\:\mathrm{his}\:\mathrm{friends}\:\mathrm{receive}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{letters}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{4}\:\mathrm{receive}\:\mathrm{the}\:\mathrm{wrong}\:\mathrm{ones}. \\ $$ Answered by mr W last updated on 22/Mar/21 $${p}=\frac{{P}_{\mathrm{3}}…

Question-136417

Question Number 136417 by I want to learn more last updated on 21/Mar/21 Answered by EDWIN88 last updated on 22/Mar/21 $$\mathrm{even}\:\mathrm{number}\:=\:\left\{\mathrm{2},\mathrm{4}\right\}\:,\:\mathrm{odd}\:\mathrm{number}=\left\{\mathrm{1},\mathrm{3},\mathrm{5}\right\} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\mathrm{on}\:\mathrm{two}\:\mathrm{balls} \\ $$$$\mathrm{have}\:\mathrm{probabability}\:=\:\frac{\mathrm{1}+\mathrm{3}}{\mathrm{C}_{\mathrm{2}}…

A-delegation-of-4-people-is-to-be-selected-from-5-women-and-6-men-Find-the-number-of-possible-delegations-if-a-there-are-no-restrictions-b-there-is-at-least-1-woman-c-there-are-at-least-2-w

Question Number 5280 by Rasheed Soomro last updated on 04/May/16 $$\mathrm{A}\:\mathrm{delegation}\:\mathrm{of}\:\mathrm{4}\:\mathrm{people}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{selected}\:\mathrm{from}\:\mathrm{5}\:\mathrm{women}\:\mathrm{and}\:\mathrm{6}\:\:\mathrm{men}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{delegations}\:\mathrm{if} \\ $$$$\left(\boldsymbol{\mathrm{a}}\right)\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{restrictions}, \\ $$$$\:\left(\boldsymbol{\mathrm{b}}\right)\:\mathrm{there}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least}\:\mathrm{1}\:\mathrm{woman}, \\ $$$$\left(\boldsymbol{\mathrm{c}}\right)\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least}\:\mathrm{2}\:\mathrm{women}. \\ $$$$\mathrm{One}\:\mathrm{of}\:\mathrm{the}\:\mathrm{men}\:\mathrm{cannot}\:\mathrm{get}\:\mathrm{along}\:\mathrm{with}\:\: \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}…

Question-5275

Question Number 5275 by sanusihammed last updated on 03/May/16 Answered by Rasheed Soomro last updated on 04/May/16 $$\mathrm{Three}\:\mathrm{members}\:\mathrm{of}\:\mathrm{the}\:\mathrm{commetee}\:\mathrm{of}\:\mathrm{six} \\ $$$$\mathrm{are}\:\mathrm{chairman},\:\mathrm{secratery}\:\mathrm{and}\:\mathrm{treasurer}. \\ $$$$\mathrm{Remaining}\:\mathrm{3}\:\mathrm{members}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{out}\:\mathrm{of} \\ $$$$\mathrm{7}\:\mathrm{members}: \\…

Calculate-the-number-of-ways-in-which-a-5-children-can-be-divided-into-groups-of-2-and-3-b-9-children-can-be-divided-into-groups-of-5-and-4-Hence-calculate-the-number-of-ways-in-which-9-childre

Question Number 5254 by Rasheed Soomro last updated on 02/May/16 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\left(\boldsymbol{\mathrm{a}}\right)\:\mathrm{5}\:\mathrm{children}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups} \\ $$$$\mathrm{of}\:\mathrm{2}\:\mathrm{and}\:\mathrm{3}\:, \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\mathrm{9}\:\mathrm{children}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups} \\ $$$$\mathrm{of}\:\mathrm{5}\:\mathrm{and}\:\mathrm{4}, \\ $$$$\mathrm{Hence}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in} \\ $$$$\mathrm{which}\:\mathrm{9}\:\mathrm{children}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into} \\ $$$$\mathrm{groups}\:\mathrm{of}\:\mathrm{2},\mathrm{3}\:\mathrm{and}\:\mathrm{4}.…