Given this question,
the part im hung up on is the "can not be distinguished part"
I would think you would take
14 total
and split into
triplets = 6 ppl
twins = 6 ppl
individuals = 2 ppl
and since they cant be distinguished from one another you would just do
3!
but thats not the answer.
what you actually have to do is
6! * 6! * 2! = 1,036,800
the part im having trouble wrapping my head around is what exactly this means if acted out.
is it saying
group 1 : can arrange 6 people 720 ways
group 2 : can arrange 6 people 720 ways
group 3 : can arrange 2 people 2 ways
what i picture this meaning is :
first 6 chairs could go 720 different ways ( all triplets in chair 1-6)
next 6 chairs could go 720 different ways ( all twins in chair 7-12)
last 2 chairs could go 2 different ways ( individuals in chair 13, 14)
is this not accounting for when they move out of order? like a twin sits in chair 2 and a individual sits in chair 5 like wise theres a triplet in chair 9 and 13?
or is that exactly what the multiplication is doing?
you have 720 different choices * 720 different choices * 2 choices?
I guess i dont see how this is mixing them together. and to what end? why is the answer not just 14! then?
if it was addition, 720+720+2 that would keep the people in their certain sections?
i feel like imthis close to understanding this but cant quite grasp it
any insight would be greatly appreciated, thanks
also -- holy **** this doesnt make any sense,
if there are "two sets of identical triplets, and three sets of identical twins" that are indistinguishable...... that makes zero sense because 2 sets or identical triplets couldn't possibly be indistinguishable, 3 triplets happen to look EXACTLY like 3 other triplets? isnt that genetically impossible?
I dont want to spark some political incorrectness but wouldn't this be easier to think of as like...
blue people, green people and red people? idk...
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