mathmath333
  • mathmath333
Counting Problem
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can 4 boys & 4 girls be arranged}\hspace{.33em}\\~\\ & \normalsize \text{such that no 2 girls are together.}\hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
You can probably make an organized list, or sample space
mathmath333
  • mathmath333
ok

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More answers

mathmath333
  • mathmath333
3 girls together also includes 2 girls together
mathmath333
  • mathmath333
u mean answer is 2
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can 4 boys & 4 girls be arranged in a row}\hspace{.33em}\\~\\ & \normalsize \text{such that no 2 girls are together.}\hspace{.33em}\\~\\ \end{align}}\)
ganeshie8
  • ganeshie8
forget about girls, first you arrange the \(4\) boys
ganeshie8
  • ganeshie8
how many ways can you arrange \(4\) boys ?
mathmath333
  • mathmath333
4!=24
ganeshie8
  • ganeshie8
Yes |dw:1440079075919:dw|
anonymous
  • anonymous
don't mind me - I am not good with this stuff - just read/listen to what @ganeshie8 wrote
mathmath333
  • mathmath333
5*4=20
IrishBoy123
  • IrishBoy123
.
ganeshie8
  • ganeshie8
scratch that
mathmath333
  • mathmath333
have u also counted this situation gbbgbgbg
ganeshie8
  • ganeshie8
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 : |dw:1440079754229:dw|
ganeshie8
  • ganeshie8
how many ways can you arrange 4 girls in 5 chairs ?
IrishBoy123
  • IrishBoy123
.
ganeshie8
  • ganeshie8
In other words, how many 4 letter words can you make using 5 different letters ?
mathmath333
  • mathmath333
4!
ganeshie8
  • ganeshie8
no, try again
mathmath333
  • mathmath333
5!
ganeshie8
  • ganeshie8
yes so the final answer is \(4!*5!\)
mathmath333
  • mathmath333
is their any alternate way for this
ganeshie8
  • ganeshie8
there are many ways to work it the one i showed you is the most simplest one
mathmath333
  • mathmath333
example using negation of sentense "no 2 girls are together"
ganeshie8
  • ganeshie8
that would only complicate things because you need to consider different cases : 2 girls together, 3 girls together, 4 girls together
ganeshie8
  • ganeshie8
the method i showed you is simple : 1) first place boys 2) next work out where girls can go

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