SOLUTION: How many ways can you make a change for a dollar using no pennies and at most 1 nickel? Please help I am confused. Thanks

Question 133975: How many ways can you make a change for a dollar using no pennies and at most 1 nickel? Please help I am confused. Thanks
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You don't say whether $1.00 and/or $0.50 coins are available. Let's exclude the $1.00 coin because that is trivial. So you have four different coins available, half-dollar, quarter, dime, and at most one nickel.

You could use two half dollars

You could use one half dollar and two quarters

One half dollar, one quarter, two dimes and one nickel

One half dollar, no quarters, and five dimes

(You can't have one half dollar, no quarters, four dimes and two nickels because that violates the 'one nickel' rule)

No half dollars, three quarters, two dimes, one nickel

No half dollars, two quarters, five dimes

No half dollars, one quarter, seven dimes, one nickel

Ten dimes

All together, 8 ways. If you don't have half dollar coins, then only count the ways that don't use half dollars, total 4.
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