ANSWER:
See below. Combinations that differ only in the number of nickels and pennies
used are shown on a single line with the total number of combinations in parentheses (to save space). For
example, in the last combination, there are 21 different ways to make $1.00 using only nickels and pennies
(using 0 to 20 nickels and the rest pennies).
There is
1 combination where TWO half dollars are used:
2 half dollars
There are
49 combinations where ONE half dollar is used:
1 half dollar, 2 quarters (1 way)
1 half dollar, 1 quarter, 2 dimes (2 ways)
1 half dollar, 1 quarter, 1 dime (4 ways)
1 half dollar, 1 quarter, 0 dimes (6 ways)
1 half dollar, 0 quarters, 5 dimes (1 way)
1 half dollar, 0 quarters, 4 dimes (3 ways)
1 half dollar, 0 quarters, 3 dimes (5 ways)
1 half dollar, 0 quarters, 2 dimes (7 ways)
1 half dollar, 0 quarters, 1 dime (9 ways)
1 half dollar, 0 quarters, 0 dimes (11 ways)
There are
242 combinations where NO half dollars are used:
4 quarters (1 way)
3 quarters, 2 dimes (2 ways)
3 quarters, 1 dime (4 ways)
3 quarters, 0 dimes (6 ways)
2 quarters, 5 dimes (1 way)
2 quarters, 4 dimes (3 ways)
2 quarters, 3 dimes (5 ways)
2 quarters, 2 dimes (7 ways)
2 quarters, 1 dime (9 ways)
2 quarters, 0 dimes (11 ways)
1 quarter, 7 dimes (2 ways)
1 quarter, 6 dimes (4 ways)
1 quarter, 5 dimes (6 ways)
1 quarter, 4 dimes (8 ways)
1 quarter, 3 dimes (10 ways)
1 quarter, 2 dimes (12 ways)
1 quarter, 1 dime (14 ways)
1 quarter, 0 dimes (16 ways)
0 quarters, 10 dimes (1 way)
0 quarters, 9 dimes (3 ways)
0 quarters, 8 dimes (5 ways)
0 quarters, 7 dimes (7 ways)
0 quarters, 6 dimes (9 ways)
0 quarters, 5 dimes (11 ways)
0 quarters, 4 dimes (13 ways)
0 quarters, 3 dimes (15 ways)
0 quarters, 2 dimes (17 ways)
0 quarters, 1 dimes (19 ways)
0 quarters, 0 dimes (21 ways)
