You have a coin each of the denominations 1 cent, 5 cents, 10 cents, 20 cents and 50 cents.

Question

How many different amounts greater than 20 cents can you form by choosing any two of these coins?

Answer 1

Just to list them, take the coins in order

from smallest to largest denomination pairing

them with all coins that will total more than $.20

 

Note that .05 + .25 is the same as

.25 + .05 so no backtracking is needed.

 

.01, .05, .10, .25, .50 coins... 1 each

 

.01+ .25

.01 + .50

.05 + .25

.05 + .50

.10 + .25

.10 + .50

.25 + .50

 

7 combinations

Answer 2

This is a combinations type of problem.  

 

However, may I first point out that there is no 20 cent coin, so let's assume that 25 cent coin was intended.

 

The answer will be 5C2, which is ten...for all combinations involving any two coins.  However, we must rule out all of the following pairs:

1,5

1,10

5,10

 

This gives us the final answer, 7.