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In-how-many-ways-can-4-boys-and-3-girls-stand-in-a-straight-line-a-if-there-are-no-restrictions-b-if-the-boys-stand-next-to-each-other-




Question Number 56212 by pieroo last updated on 12/Mar/19
In how many ways can 4 boys and 3 girls  stand in a straight line  a. if there are no restrictions  b. if the boys stand next to each other
$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls} \\ $$$$\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{a}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{restrictions} \\ $$$$\mathrm{b}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{stand}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 12/Mar/19
a)for no restrictiin...7!=5040  b)let four boys faviquicked...  (b_1 b_2 b_3 b_4 ) ←it considered single unit  so permutation is (1+3)!×4!=576
$$\left.{a}\right){for}\:{no}\:{restrictiin}…\mathrm{7}!=\mathrm{5040} \\ $$$$\left.{b}\right){let}\:{four}\:{boys}\:{faviquicked}… \\ $$$$\left({b}_{\mathrm{1}} {b}_{\mathrm{2}} {b}_{\mathrm{3}} {b}_{\mathrm{4}} \right)\:\leftarrow{it}\:{considered}\:{single}\:{unit} \\ $$$${so}\:{permutation}\:{is}\:\left(\mathrm{1}+\mathrm{3}\right)!×\mathrm{4}!=\mathrm{576} \\ $$$$ \\ $$
Commented by pieroo last updated on 12/Mar/19
Thank you very much sir.
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{sir}. \\ $$

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