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 bybobhans 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 bybemath last updated on 04/Jul/20

what the formula?

Answered by bobhans last updated on 04/Jul/20

24 ways

Commented bybobhans last updated on 04/Jul/20

M_M_M_M_ ⇔ P_4 ^4  = ((4!)/((4−4)!)) = 24 ★

Commented bymr W last updated on 04/Jul/20

can you give some explanation to  the formula sir?

Answered by mr W last updated on 04/Jul/20

case 1: XMXMXMXM  ⇒((4!)/(2!2!))=6  case 2: MXMXMXMX  ⇒((4!)/(2!2!))=6  case 3: MXYMXMXM, MXMXYMXM, MXMXMXYM  ⇒3×2×2=12    totally: 6+6+12=24

Answered by john santu last updated on 05/Jul/20

If the math books are in position  1/3/5/7 or 2/4/6/8 there are  6 ways to arrange the physics  and the chemistry → 2×6 = 12  but if the math books are in  position 1/3/5/8 or 1/3/6/8   or 1/4/6/8 then there are only  4 way → 3×4 =12  so totally = 24 ways  (JS ⊛)