How many different ways are there to make 30 cents with pennies nickels dimes or quarters?

There is 1 way to make 30 cents using only pennies. (i.e. 30 pennies = 30 cents)

There is 1 way to make 30 cents using only nickels. (i.e. 6 nickels = 30 cents)

There is 1 way to make 30 cents using only dimes. (i.e. 3 dimes = 30 cents)

There are 5 ways to make 30 cents using only pennies and nickels. (i.e. 25 pennies + 1 nickel = 30 cents, 20 pennies + 2 nickels = 30 cents . . . )

There are 2 ways of making 30 cents using only pennies and dimes. (i.e. 20 pennies + 1 dime = 30 cents, 10 pennies + 2 dimes = 30 cents)

There is 1 way of making 30 cents using only pennies and quarters. (i.e. 5 pennies + 1 quarter = 30 cents)

There are 2 ways of making 30 cents using only nickels and dimes. (i.e. 4 nickels + 1 dime = 30 cents, 2 nickels + 2 dimes = 30 cents)

There is 1 way of making 30 cents using only nickels and quarters. (i.e. 1 nickel + 1 quarter = 30 cents)

There are 4 ways to make 30 cents using only pennies, nickels and dimes. (i.e. 15 pennies + 1 nickel + 1 dime = 30 cents, 10 pennies + 2 nickels + 1 dime = 30 cents . . . )

Adding all the possible combinations therefore, there are 18 different ways are there to make 30 cents with pennies nickels dimes or quarters.