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Question Number 31591 by Tinkutara last updated on 10/Mar/18

Commented by mrW2 last updated on 11/Mar/18

$$noanswerseemstobecorrect$$

Commented by Tinkutara last updated on 11/Mar/18

$$YesIalsothink.Doesitshouldbe$$$${}^7{P}_4\times 6!?$$

Commented by mrW2 last updated on 11/Mar/18

$$toarrangethe6boys:$$$$6!ways$$$$toarrange4girlsinto7positions:$$$$P_4^{7}ways$$$$$$$$\Rightarrow 6!\times P_4^7=840\times 6!=120\times 7!$$

Commented by Tinkutara last updated on 11/Mar/18

Thank you very much Sir! I got the answer. ������☺

Answered by MJS last updated on 11/Mar/18

$$\mathrm{the}\mathrm{girls}\mathrm{can}\mathrm{be}\mathrm{on}\mathrm{these}\mathrm{positions}$$$$\left(0\mathrm{stands}\mathrm{for}10\right):$$$$1357135813591350$$$$136813691360$$$$13791370$$$$1380$$$$146814691460$$$$14791470$$$$1480$$$$15791570$$$$1580$$$$1680$$$$246824692460$$$$24792470$$$$2480$$$$25792570$$$$2580$$$$2680$$$$35793570$$$$3580$$$$3680$$$$4680$$$$\mathrm{so}{\mathrm{it}}^{\prime }\mathrm{s}35\times 4!\times 6!=5\times 7\times 4!\times 6!=$$$$=5!\times 7!$$

Commented by mrW2 last updated on 11/Mar/18

$$thisismysolution:$$$$betweentwogirlstheremustbeat$$$$leastoneboy,{that}^{\prime }stosaythefour$$$$girlscanonlybeplacedinthepositions$$$$markedas⊝:$$$$⊝⊛⊝⊛⊝⊛⊝⊛⊝⊛⊝⊛⊝$$$$where⊛meansaboy.$$$$$$$$followingise.g.avalidarrangement:$$$$⊝⊛◻⊛⊝⊛◻⊛◻⊛⊝⊛◻$$$$where◻meansagirl,⊝meansempty.$$$$$$$$toarrangethe6boys⊛:6!ways$$$$toarrangethe4girls◻:P_4^{7}ways$$$$\Rightarrow result=P_4^7\times 6!ways.$$$$$$$$generally:nstudents,mgirls$$$$\Rightarrow P_m^{n-m+1}\times (n-m)!$$

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