Question

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?

Answer 1

what

Answer 2

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

Answer 3

_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?

Answer 4

yes 6!/3!

Answer 5

what about this cases

KQR- - -
-KQR- -
K- Q- - R

Answer 6

_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.

Answer 7

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!

Answer 8

ok thnks

Answer 9

what about the question u posted yesterday :)

Answer 10

http://openstudy.com/users/mathmath333#/updates/55f52326e4b0cf7fa75bbeb9

Answer 11

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

Answer 12

:) wise ( ͡° ͜ʖ ͡°)

but maybe theres some trick still hidden somewhere :)

Answer 13

I will not trust any trick , another conclusion

Answer 14

:)

Answer 15

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.

Answer 16

question is closed

Answer 17

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

Answer 18

I'll ask my prof for a soln

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

kewl :D