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?

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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?

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

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yes 6!/3!
what about this cases KQR- - - -KQR- - K- Q- - R
_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.
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!
ok thnks
what about the question u posted yesterday :)
I made a conclusion if such question comes in exam i will leave it unsolved and move to next easy question
:) wise ( ͡° ͜ʖ ͡°) but maybe theres some trick still hidden somewhere :)
I will not trust any trick , another conclusion
:)
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.
question is closed
It's ok. I'll keep looking at my end!
I'll ask my prof for a soln
@mathmath333 Thank you. Btw, have you done generating functions yet?
No, this sounds a higher level maths to me. I haven't studied calculus .
It's part of combinatorics, NCR (no calculus required). That might be a hint for me where to look though. xD
lol i m a newbie in case of math , i only learn things that matters to me
kewl :D

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