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 21929 by Tinkutara last updated on 07/Oct/17

There are 8 Hindi novels and 6 English novels. 4 Hindi novels and 3 English novels are selected and arranged in a row such that they are alternate then no. of ways is

$$\mathrm{There}\:\mathrm{are}\:\mathrm{8}\:\mathrm{Hindi}\:\mathrm{novels}\:\mathrm{and}\:\mathrm{6}\:\mathrm{English} \\ $$$$\mathrm{novels}.\:\mathrm{4}\:\mathrm{Hindi}\:\mathrm{novels}\:\mathrm{and}\:\mathrm{3}\:\mathrm{English} \\ $$$$\mathrm{novels}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{and}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{alternate}\:\mathrm{then} \\ $$$$\mathrm{no}.\:\mathrm{of}\:\mathrm{ways}\:\mathrm{is} \\ $$

Commented by mrW1 last updated on 07/Oct/17

to select 4 from 8 hindi novels there are C_4 ^8 possibilities to select 3 from 6 english novels there are C_3 ^6 possibilities since the 4 hindi novels and 3 english novels must alternate in a row, they can only be placed like this: HEHEHEH to arrange the 4 selected hindi novels there are 4! possibilities to arrange the 3 selected english novels there are 3! possibilities ⇒total ways: C_4 ^8 ×C_3 ^6 ×4!×3!=201600

$$\mathrm{to}\:\mathrm{select}\:\mathrm{4}\:\mathrm{from}\:\mathrm{8}\:\mathrm{hindi}\:\mathrm{novels}\:\mathrm{there} \\ $$$$\mathrm{are}\:\mathrm{C}_{\mathrm{4}} ^{\mathrm{8}} \:\mathrm{possibilities} \\ $$$$ \\ $$$$\mathrm{to}\:\mathrm{select}\:\mathrm{3}\:\mathrm{from}\:\mathrm{6}\:\mathrm{english}\:\mathrm{novels}\:\mathrm{there} \\ $$$$\mathrm{are}\:\mathrm{C}_{\mathrm{3}} ^{\mathrm{6}} \:\mathrm{possibilities} \\ $$$$ \\ $$$$\mathrm{since}\:\mathrm{the}\:\mathrm{4}\:\mathrm{hindi}\:\mathrm{novels}\:\mathrm{and}\:\mathrm{3}\:\mathrm{english}\:\mathrm{novels} \\ $$$$\mathrm{must}\:\mathrm{alternate}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row},\:\mathrm{they}\:\mathrm{can}\:\mathrm{only} \\ $$$$\mathrm{be}\:\mathrm{placed}\:\mathrm{like}\:\mathrm{this}: \\ $$$$\mathrm{HEHEHEH} \\ $$$$ \\ $$$$\mathrm{to}\:\mathrm{arrange}\:\mathrm{the}\:\mathrm{4}\:\mathrm{selected}\:\mathrm{hindi}\:\mathrm{novels} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{4}!\:\mathrm{possibilities} \\ $$$$ \\ $$$$\mathrm{to}\:\mathrm{arrange}\:\mathrm{the}\:\mathrm{3}\:\mathrm{selected}\:\mathrm{english}\:\mathrm{novels} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{3}!\:\mathrm{possibilities} \\ $$$$ \\ $$$$\Rightarrow\mathrm{total}\:\mathrm{ways}: \\ $$$$\mathrm{C}_{\mathrm{4}} ^{\mathrm{8}} ×\mathrm{C}_{\mathrm{3}} ^{\mathrm{6}} ×\mathrm{4}!×\mathrm{3}!=\mathrm{201600} \\ $$

Commented by Tinkutara last updated on 07/Oct/17

Thank you very much Sir!

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir}! \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com