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Question Number 56212 by pieroo last updated on 12/Mar/19
$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls} \\ $$$$\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{a}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{restrictions} \\ $$$$\mathrm{b}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{stand}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 12/Mar/19
$$\left.{a}\right){for}\:{no}\:{restrictiin}...\mathrm{7}!=\mathrm{5040} \\ $$$$\left.{b}\right){let}\:{four}\:{boys}\:{faviquicked}... \\ $$$$\left({b}_{\mathrm{1}} {b}_{\mathrm{2}} {b}_{\mathrm{3}} {b}_{\mathrm{4}} \right)\:\leftarrow{it}\:{considered}\:{single}\:{unit} \\ $$$${so}\:{permutation}\:{is}\:\left(\mathrm{1}+\mathrm{3}\right)!×\mathrm{4}!=\mathrm{576} \\ $$$$ \\ $$
Commented by pieroo last updated on 12/Mar/19
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{sir}. \\ $$