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Question Number 56212 by pieroo last updated on 12/Mar/19

$$\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{ways}\mathrm{can}4\mathrm{boys}\mathrm{and}3\mathrm{girls}$$$$\mathrm{stand}\mathrm{in}\mathrm{a}\mathrm{straight}\mathrm{line}$$$$\mathrm{a}.\mathrm{if}\mathrm{there}\mathrm{are}\mathrm{no}\mathrm{restrictions}$$$$\mathrm{b}.\mathrm{if}\mathrm{the}\mathrm{boys}\mathrm{stand}\mathrm{next}\mathrm{to}\mathrm{each}\mathrm{other}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 12/Mar/19

$$a)fornorestrictiin...7!=5040$$$$b)letfourboysfaviquicked...$$$$\left(b_1{b}_2{b}_3{b}_4\right)\leftarrow itconsideredsingleunit$$$$sopermutationis(1+3)!\times 4!=576$$$$$$

Commented by pieroo last updated on 12/Mar/19

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{sir}.$$

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