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Category: Permutation and Combination

Prove-by-induction-the-following-result-where-N-is-a-positive-even-integer-S-1-2-S-2-2-2-N-where-S-1-r-1-N-2-1-1-r-1

Question Number 1074 by Yugi last updated on 05/Jun/15 ProvebyinductionthefollowingresultwhereNisapositiveeveninteger.S12+S22=2N$${where}\:\:\:\:{S}_{\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{\frac{{N}}{\mathrm{2}}+\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} (N2(r1))\:\:\:\:{and}\:\:\:\:\:\:{S}_{\mathrm{2}} =\underset{{r}=\mathrm{1}} {\overset{{N}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{{r}+\mathrm{1}}…

Eight-people-are-seated-around-a-circular-table-Each-person-must-shake-everyone-s-hand-but-they-must-not-shake-hands-with-the-two-persons-seated-at-their-sides-How-many-handshakes-occur-

Question Number 911 by 112358 last updated on 22/Apr/15 Eightpeopleareseatedaroundacirculartable.Eachpersonmustshakeeveryoneshandbuttheymustnotshakehandswiththetwopersonsseatedattheirsides.Howmanyhandshakesoccur? Answered by prakash…

three-subject-group-are-to-be-formed-randomly-by-15-students-including-3-girls-under-the-condition-that-each-groups-consist-5-students-and-each-student-attends-only-one-group-flnd-the-probabilitie

Question Number 131635 by liberty last updated on 07/Feb/21 threesubjectgrouparetobeformedrandomlyby15students(including3girls)undertheconditionthateachgroupsconsist5studentsandeachstudentattendsonlyonegroup.$$\mathrm{flnd}\:\mathrm{the}\:\mathrm{probabilities}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the} \