Question 1030866: A jar contains pennies, nickels, dimes, and quarters. Without looking or feeling, you take three of the coins.
A.) List all possible sets of three coins you might select
B.) List all possible three coin total value you might select
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source):
Answer by ikleyn(52925)  (Show Source):
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A jar contains pennies, nickels, dimes, and quarters. Without looking or feeling, you take three of the coins.
A) List all possible sets of three coins you might select
B) List all possible three coin total value you might select
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The first sentence says "A jar contains pennies, nickels, dimes, and quarters."
It does not tell, how many such coins of every type are there in the jar.
By DEFAULT, we should assume that the number of each kind of coins is LARGE ENOUGH.
If consider different triples of coins without repetition of types inside each triple,
then we have classic COMBINATIONS, and the number of such triples is  = 4.
But repetitions inside each triple ARE NOT PROHIBITED: they are allowed.
So, we should add such triples with repetitions.
Triples with repetitions are
a) (X, X, Y), where X can be any of 4 types and Y can be any of other 3 types.
In all, there are 4*3 = 12 such triples (disregarding the order inside the triples).
b) to it, we should add 4 triples of the form (X, X, X), where X can be any of 4 types.
Taking everything into account, we have, in all, 4 + 12 + 4 = 20 possible different triples (disregarding the order inside the triples).
ANSWER. there are 20 possible different triples, disregarding the order inside the triples.
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