Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 123878 by liberty last updated on 29/Nov/20

Nine chairs in a row are to be occupied by  six students and Prof George , Prof Pieter,  and Prof John. These three professors arrive  before the six students and decide to choose  their chairs so that each professor will be between  two students. In how many ways can Professor George  , Pieter and John choose their chairs ?

$${Nine}\:{chairs}\:{in}\:{a}\:{row}\:{are}\:{to}\:{be}\:{occupied}\:{by} \\ $$$${six}\:{students}\:{and}\:{Prof}\:{George}\:,\:{Prof}\:{Pieter}, \\ $$$${and}\:{Prof}\:{John}.\:{These}\:{three}\:{professors}\:{arrive} \\ $$$${before}\:{the}\:{six}\:{students}\:{and}\:{decide}\:{to}\:{choose} \\ $$$${their}\:{chairs}\:{so}\:{that}\:{each}\:{professor}\:{will}\:{be}\:{between} \\ $$$${two}\:{students}.\:{In}\:{how}\:{many}\:{ways}\:{can}\:{Professor}\:{George} \\ $$$$,\:{Pieter}\:{and}\:{John}\:{choose}\:{their}\:{chairs}\:?\: \\ $$

Answered by john_santu last updated on 29/Nov/20

 let ⊕=place  for 3 professor           △=place for student  △△⊕△△⊕△△⊕△△⊕△△⊕  = P_3 ^( 5)  = ((5!)/(2!)) = 60 ways

$$\:{let}\:\oplus={place}\:\:{for}\:\mathrm{3}\:{professor} \\ $$$$\:\:\:\:\:\:\:\:\:\bigtriangleup={place}\:{for}\:{student} \\ $$$$\bigtriangleup\bigtriangleup\oplus\bigtriangleup\bigtriangleup\oplus\bigtriangleup\bigtriangleup\oplus\bigtriangleup\bigtriangleup\oplus\bigtriangleup\bigtriangleup\oplus \\ $$$$=\:{P}_{\mathrm{3}} ^{\:\mathrm{5}} \:=\:\frac{\mathrm{5}!}{\mathrm{2}!}\:=\:\mathrm{60}\:{ways} \\ $$$$ \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com