Values From Three Coins

How many possible values can there be for three coins selected from among pennies, nickels, dimes, and quarters.
Source: NCTM Mathematics Teacher, August 2006

Solution
a) All three coins are the same
1\:1\:1
5\:5\:5
10\:10\:10
25\:25\:25
Number of ways = 4
b) Two of the coins are the same
1\:1\:-
-\:1\:1
1\:-\:1
\cdots
Number of ways = 3\times 4=12
c) All three coins are different
Number of ways = \dbinom {4}{3}=4
Total number of ways = 4+12+4=20
If we check the values of these 20 ways, the values are all different. There are 20 possible values when three coins are selected from among pennies, nickels, dimes, and quarters.

Answer: 20

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About mvtrinh

Retired high school math teacher.
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