Counting Problem

Question

Counting Problem

mathmath333 · Answer

$\large \color{black}{\begin{align}
& \normalsize \text{In how many ways can 4 boys & 4 girls be arranged}\hspace{.33em}\~\
& \normalsize \text{such that no 2 girls are together.}\hspace{.33em}\~\
\end{align}}$

anonymous · Answer

You can probably make an organized list, or sample space

mathmath333 · Answer

ok

mathmath333 · Answer

3 girls together also includes 2 girls together

mathmath333 · Answer

u mean answer is 2

mathmath333 · Answer

$\large \color{black}{\begin{align}
& \normalsize \text{In how many ways can 4 boys & 4 girls be arranged in a row}\hspace{.33em}\~\
& \normalsize \text{such that no 2 girls are together.}\hspace{.33em}\~\
\end{align}}$

ganeshie8 · Answer

forget about girls,
first you arrange the $4$ boys

ganeshie8 · Answer

how many ways can you arrange $4$ boys ?

mathmath333 · Answer

4!=24

ganeshie8 · Answer

Yes
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anonymous · Answer

don't mind me - I am not good with this stuff - just read/listen to what @ganeshie8 wrote

mathmath333 · Answer

5*4=20

irishboy123 · Answer

.

ganeshie8 · Answer

scratch that

mathmath333 · Answer

have u also counted this situation

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ganeshie8 · Answer

next, for each of that arrangement,
the girls can only go between the boys.

so there are exactly $5$ for the $4$ girls to go : 

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