Question 1163048
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Depends on whether the order of the boys and the order of the girls matters.  In other words, is Billy, Bobby, Brett, Brandon, Bozo a different arrangement than Brandon, Bozo, Billy, Brett, Bobby?


If order doesn't matter, then there are 2 arrangements. Either all 5 boys are first followed by the 4 girls, or all 4 girls are first followed by the boys.


Otherwise, the boys can be arranged in *[tex \Large 5!] ways and the girls in *[tex \Large 4!] ways. So if the boys come first, there are *[tex \Large 5!\,\cdot\,4!] ways, and if the girls come first, there are *[tex \Large 4!\,\cdot\,5!] ways.  Altogether, there are *[tex \Large 2\,\cdot\,\Large 5!\,\cdot\,4!] ways.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
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