mathmath333
  • mathmath333
The number of ways in which four particular persons A,B,C,D and six more persons can stand in a queue so that A always stands before B, B before C, and C before D, is ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{ The number of ways in which four particular persons A,B,C,D }\hspace{.33em}\\~\\ & \normalsize \text{ and six more persons can stand in a queue so that A always }\hspace{.33em}\\~\\ & \normalsize \text{ stands before B, B before C, and C before D, is ? }\hspace{.33em}\\~\\ \end{align}}\)
dan815
  • dan815
|dw:1442643874411:dw|
mathmath333
  • mathmath333
this is one of the case

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mathmath333
  • mathmath333
|dw:1442644105548:dw|
dan815
  • dan815
10!/4!
dan815
  • dan815
there are 10! ways to arrange these 10 persons now for each of those arrangements there is some arrangement of ABCD 4! ways of them, we only want the arrangement A B C D so 1 for every one of thsoe 4! ways thus 10!/4!
mathmath333
  • mathmath333
but the ABCD can be in many ways like this |dw:1442644275123:dw|
dan815
  • dan815
do you want clearer explaination
dan815
  • dan815
for example lets take some random arrangement in 10! 1 2 3 4 A 5 B 6 C D okay for this arrangement there are 4! other ways we count when A B C D can be placed in way , and the numbers 1 to 6 are left in same spot
mathmath333
  • mathmath333
is this (below) a valid set up|dw:1442644423498:dw|
dan815
  • dan815
we count that in the 10!
dan815
  • dan815
so taking 1 for every 4! we will take only the A B C D case for each of those arrangements in 10!
mathmath333
  • mathmath333
ok
dan815
  • dan815
you have any questions about this?
mathmath333
  • mathmath333
let me read and think
dan815
  • dan815
ill make it clearer okay
dan815
  • dan815
for 10! ways we will have the arrangement of every single possible way of placing these 10 people
dan815
  • dan815
let us look at some of these arragenment sequences
dan815
  • dan815
|dw:1442644766778:dw|
dan815
  • dan815
there are 4! ways for this one arrangement of how you play these 6 people in the 10 spots
dan815
  • dan815
out of these 4! ways , we only want one of them where its A B C D
dan815
  • dan815
so another way less intuitive would now be this means all we care about is how we place the 6 people in the 10 spots
mathmath333
  • mathmath333
ok i got it
dan815
  • dan815
ok
mathmath333
  • mathmath333
|dw:1442645081498:dw|
dan815
  • dan815
welcome!

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