mathmath333 one year ago Their are 6 pieces king,queen,rook bishop,knight and pawn.In how many ways can u arrange them so that king always comes before queen and queen always comes before rook?

1. anonymous

what

2. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{Their are 6 pieces king,queen,rook bishop,knight }\hspace{.33em}\\~\\ & \normalsize \text{and pawn.In how many ways can u arrange them }\hspace{.33em}\\~\\ & \normalsize \text{so that king always comes before queen and queen }\hspace{.33em}\\~\\ & \normalsize \text{always comes before rook? }\hspace{.33em}\\~\\ \end{align}}

3. mathmate

_K_Q_R_ 4 ways to put the bishop 5 ways to put the knight 6 ways to put the pawn. 120 ways. Would that be right?

4. mathmath333

yes 6!/3!

5. mathmath333

6. mathmate

_K_Q_R_ Say put the biship after R then we have _K_Q_R_B_ that's why 5 places for knight. Say _K_Q_R_B_N_ and the pawn chooses to be last, then _K_Q_R_B_N_P_ (if there is a seventh) so that gives the case KQR___ similarly for other situations.

7. mathmate

Or, another way to look at it, it would be 6! ways in general, but we will tag the 3! arrangements of KQR and use only one, so the result would be 6!/3! as you had it. This is a combinatorial verification!

8. mathmath333

ok thnks

9. imqwerty

what about the question u posted yesterday :)

10. mathmath333
11. mathmath333

I made a conclusion if such question comes in exam i will leave it unsolved and move to next easy question

12. imqwerty

:) wise ( ͡° ͜ʖ ͡°) but maybe theres some trick still hidden somewhere :)

13. mathmath333

I will not trust any trick , another conclusion

14. imqwerty

:)

15. mathmate

I hope someone will post a smarter and faster solution. Although that one doesn't take long, it looks complicated, but detailed for the purpose of explaining only.

16. mathmath333

question is closed

17. mathmate

It's ok. I'll keep looking at my end!

18. mathmath333

I'll ask my prof for a soln

19. mathmate

@mathmath333 Thank you. Btw, have you done generating functions yet?

20. mathmath333

No, this sounds a higher level maths to me. I haven't studied calculus .

21. mathmate

It's part of combinatorics, NCR (no calculus required). That might be a hint for me where to look though. xD

22. mathmath333

lol i m a newbie in case of math , i only learn things that matters to me

23. imqwerty

kewl :D