Jay03Ceredonviz
Answered

in how many ways can you arrange 4 boys and 3 girls alternately in a row?
a. 362,880 b.24 c.48 d.768​

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[tex] \blue{\bold{ANSWER : }}[/tex]

  • [tex] \blue{\boxed{\bold{B. \: _4P_3= 24}}}[/tex]

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Given:

  • [tex] \tt n = 4 \: boys \: || \: r = 3 \: girls[/tex]

[tex] \blue{\bold{SOLUTION : }}[/tex]

To find if how many ways can be arranged the 4 boys and 3 girls by using linear permutation formula. Apply the n and r.

  • [tex] \tt _nP_3 = \frac{n!}{(n - r)!} [/tex]

  • [tex] \tt _4P_3= \frac{4!}{(4 - 3)!} [/tex]

  • [tex] \tt _4P_3 = \frac{4!}{1!} [/tex]

  • [tex] \tt _4P_3= \frac{4!}{1} [/tex]

  • [tex] \tt _4P_3= 4! [/tex]

  • [tex] \blue {\boxed {\tt {{_4P_r = 24}}}}[/tex]

Therefore, there are 24 ways can I arranged 4 boys and 3 girls alternately in a row.

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Hope it's help!