Question 731856: 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?
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176)   (Show Source):
Answer by ikleyn(53418)  (Show Source):
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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.
First, we select 3 boys from 6 boys to place them into the 1st canoe.
It can be done in C(6,3) =  = 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) = = 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.
ANSWER. 144 different arrangements are possible under accepted assumptions.
No one more and no one less than that.
Solved, with explanations.
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