Question Number 165301 by mathdave last updated on 28/Jan/22
Answered by som(math1967) last updated on 29/Jan/22
$$\mathrm{1}.\boldsymbol{{No}}\:\boldsymbol{{of}}\:\boldsymbol{{ways}}\:'\boldsymbol{{median}}'\:\boldsymbol{{be}}\:\boldsymbol{{arranged}} \\ $$$$\:\mathrm{6}!=\mathrm{720} \\ $$$$\mathrm{2}.\:\boldsymbol{{M}}\:\boldsymbol{{begin}} \\ $$$$\:\boldsymbol{{M}}\:\Box\Box\Box\Box\Box\:^{\mathrm{5}} \boldsymbol{{P}}_{\mathrm{5}} =\mathrm{120} \\ $$$$\mathrm{3}.\:\boldsymbol{{N}}\:\boldsymbol{{end}} \\ $$$$\:\:\Box\Box\Box\Box\Box\boldsymbol{{N}}\:\:\:^{\mathrm{5}} \boldsymbol{{P}}_{\mathrm{5}} =\mathrm{120} \\ $$$$\mathrm{4}.\boldsymbol{{Begin}}\:\boldsymbol{{with}}\:\boldsymbol{{M}}\:\boldsymbol{{and}}\:\boldsymbol{{end}}\:\boldsymbol{{with}}\:\boldsymbol{{N}} \\ $$$$\:\:\:\:\boldsymbol{{M}}\Box\Box\Box\Box\boldsymbol{{N}}\:\:\:\:^{\mathrm{4}} \boldsymbol{{P}}_{\mathrm{4}} =\mathrm{24} \\ $$