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Question Number 124916 by liberty last updated on 07/Dec/20

The number of ways arrangements   of the word ′MASKARA′ with exactly  2 A′s  are adjacent??

ThenumberofwaysarrangementsofthewordMASKARAwithexactly2Asareadjacent??

Answered by mr W last updated on 07/Dec/20

_M_S_K_R_  4!×P_2 ^5 =480

_M_S_K_R_4!×P25=480

Commented by mr W last updated on 07/Dec/20

Method II  3 A′s adjacent: 5!  at least 2 A′s adjacent: 6!  exactly 2 A′s adjacent: 6!−2×5!=480

MethodII3Asadjacent:5!atleast2Asadjacent:6!exactly2Asadjacent:6!2×5!=480

Commented by bemath last updated on 07/Dec/20

i got 960 sir. what wrong?

igot960sir.whatwrong?

Commented by mr W last updated on 07/Dec/20

how did you get?

howdidyouget?

Answered by liberty last updated on 07/Dec/20

(•) −_1^(st)   −^(AA)  −_2^(nd)   −^A  −_3^(rd)     Treat 4 letters M ,S, K, R as identical ′x′  since exactly 2 A′s are adjacent, one x must be  put in 2^(nd)  places ⇒ −_1^(st)   AA −_2^(nd)  ^x  A −_3^(rx)    the remaining 3 x′s can be put in  (((3+3−1)),((       3)) ) =  ((5),(3) ) = 10  (••) −_1^(st)   A −_2^(nd)   AA −_3^(rd)   similar to cases (•)  therefore the desired number of ways  is given by 2× ((5),(3) )×4! = 20×24 = 480

()1stAA2ndA3rdTreat4lettersM,S,K,Rasidenticalxsinceexactly2Asareadjacent,onexmustbeputin2ndplaces1stAAx2ndA3rxtheremaining3xscanbeputin(3+313)=(53)=10()1stA2ndAA3rdsimilartocases()thereforethedesirednumberofwaysisgivenby2×(53)×4!=20×24=480

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