The three containers are labeled incorrectly. one contains two nickels, another two pennies, and another a nickel and a penny. explain how its possible to determine the correct labeling for all three containers by selecting just one coin. using deductive reasoning.

Just one coin, hmmm
all are incorrrectly labled (this is very important
this reminds me of the puzzle from fermants room
probably the same one

pick the one that is labled "one nickle and one penny"
since all lables are incorrect, it cannot be the "one nickle and one penny"
it must be either all pennies or nickles
if you picked a nickle, that is the nickles box
if you picked a penny then that is penny box

next step
go to A if you picked a nickle
to to B if you picked a penny

A. you picked a nickle
the remaining boxes are labled 2 nickles and 2 pennies
we know one of them must be the mix and the other is pennies
incorrect lables so then the mix is in the  one labled 2 pennies and the pennies are in the one labled 2 nickles

B. you picked a penny
the remaining boxes are labled 2 nickles and 2 pennies
we know one must be the mix and the other is 2 nickles
incorrecet labels so the nickles is in the one labeld 2 pennies box and mix is in the one labeled 2 nickles box

see this website at 3rd point, basically how I got the http://support.acadsoc.com/answer-to-math-puzzles-in-fermats-room-6-177-500.html