There are 4 identical mathematics books, 2 identic physics books and 2 identical chemistry books . How many ways to compile the eight books on the condition of the same book are not mutually adjacent?


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 101693 by bemath last updated on 04/Jul/20

$There are 4 identical mathematics$ $books, 2 identic physics books$ $and 2 identical chemistry books$ $. How many ways to compile$ $the eight books on the condition$ $of the same book are not mutually$ $adjacent ?$
Commented by bobhans last updated on 04/Jul/20
MPMPMCMC, MPMCMPMC, MPMCMCMP, MCMPMPMC, MCMPMCMP, MCMCMPMP, PMPMCMCM, PMCMPMCM, PMCMCMPM, CMPMPMCM, CMPMCMPM, CMCMPMPM, MPMCMPCM, MPMCMCPM, MCMPMPCM, MCMPMCPM, MPMPCMCM, MPMCPMCM, MCMPCMPM, MCMCPMPM, MPCMPMCM, MCPMPMCM, MPCMCMPM, MCPMCMPM
Commented by bemath last updated on 04/Jul/20

$what the formula ?$
	Answered by bobhans last updated on 04/Jul/20

	$24 ways$
	Commented by bobhans last updated on 04/Jul/20

	$M_M_M_M_\Leftrightarrow P_{4}^{4} = \frac{4!}{(4 - 4)!} = 24 ★$
	Commented by mr W last updated on 04/Jul/20

	$c a n y o u g i v e s o m e e x p l a n a t i o n t o$ $t h e f o r m u l a s i r ?$
	Answered by mr W last updated on 04/Jul/20

	$c a s e 1 : X M X M X M X M$ $\Rightarrow \frac{4!}{2! 2!} = 6$ $c a s e 2 : M X M X M X M X$ $\Rightarrow \frac{4!}{2! 2!} = 6$ $c a s e 3 : M X Y M X M X M, M X M X Y M X M, M X M X M X Y M$ $\Rightarrow 3 \times 2 \times 2 = 12$ $t o t a l l y : 6 + 6 + 12 = 24$
	Answered by john santu last updated on 05/Jul/20

	$I f t h e m a t h b o o k s a r e i n p o s i t i o n$ $1 / 3 / 5 / 7 o r 2 / 4 / 6 / 8 t h e r e a r e$ $6 w a y s t o a r r a n g e t h e p h y s i c s$ $a n d t h e c h e m i s t r y \to 2 \times 6 = 12$ $b u t i f t h e m a t h b o o k s a r e i n$ $p o s i t i o n 1 / 3 / 5 / 8 o r 1 / 3 / 6 / 8$ $o r 1 / 4 / 6 / 8 t h e n t h e r e a r e o n l y$ $4 w a y \to 3 \times 4 = 12$ $s o t o t a l l y = 24 w a y s (J S ⊛)$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum