MATH DESTROYER

[csulapredental]

how many diff ways can 2 girls and 3 boys sit in a row if the 2 girls always sit side by side.
I'm trying to apply chads method but i can't tell how. clearly order matters and when order matters he just puts the number of selections on top and thats it because order matters... so it should be 5! but its not..


another one is how many ways can the same 4 physics books, 3 algebra books, and 2 chem books be arranged on a self.. again order matters so it should be 9! ??


i feel like his way isn't applying.
even if i use the equation of n!/(n-r)! there isn't a clear r to plug in!???

pelase help

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[DAT Destroyer]

how many diff ways can 2 girls and 3 boys sit in a row if the 2 girls always sit side by side.
I'm trying to apply chads method but i can't tell how. clearly order matters and when order matters he just puts the number of selections on top and thats it because order matters... so it should be 5! but its not..


another one is how many ways can the same 4 physics books, 3 algebra books, and 2 chem books be arranged on a self.. again order matters so it should be 9! ??


i feel like his way isn't applying.
even if i use the equation of n!/(n-r)! there isn't a clear r to plug in!???

pelase help

For the first one there are 4 possibilities:

ggbbb bggbb bbggb bbbgg.

Now each arrangement has 12 possibilities. Here is how: the girls can sit next to each other 2 ways. g1g2 and g2g1. For the boys it's 6 different ways or 3! Which makes it 12.
And 12*4 =48

For the second one it's :

9!/(4!3!2!).

We divide by the number of things that are similar.
These 2 questions are arrangement problems. When you say order matters, and you apply n!/(n-r)! Is when you want to select r things out of n things.

For example: how many ways can 3 runners out of 10 finish a race first, second and third?