Question 731856
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There are 6 boys,6 girls and 2 canoes. How many arrangements are possible 
where there are 3 boys in 1 canoe and 3 girls in the other canoe. Answer in book says 200?
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        In this problem, we consider the boys as distinguishable persons.


        We also consider the girls as distinguishable persons.


        We also consider canoes as distinguishable items.



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First, we select 3 boys from 6 boys to place them into the 1st canoe.

It can be done in  C(6,3) = {{{(6*4*3)/(1*2*3)}}} = 12 different ways  (combinations).


After that, three remaining boys automatically go to the 2nd canoe.


        The same with the girls.


We select 3 girls from 6 girls to place them into the 1st canoe.

It can be done in  C(6,3) = {{{(6*4*3)/(1*2*3)}}} = 12 different ways  (combinations).


After that, three remaining girls automatically go to the 2nd canoe.


Thus the number of all possible arrangements is 12 * 12 = 144.


<U>ANSWER</U>.  144 different arrangements are possible under accepted assumptions.


No one more and no one less than that.
</pre>

Solved, with explanations.