Using only 1,5;10 and 20$ bills, the number of ways that change can be made for a 75$bill is

Question

Using only 1,5, 10 and 20 dollar bills - the number of ways to make change for 75$

Answer 1

1st thing, there are no $75 bills, not in the US.

but if you want to give change to someone for their fake 75 dollar bill

easiest way with least number is

3 20s, 1 10, 1 five

other ways with 3 20s are

3 20s 3 fives

3 20s 3 fives

3 20s 2 fives 5 ones

3 20s 1 five 10 ones

3 20s 15 ones

6 ways with 3 20s

for 2 20s

2 20s 3 tens 1 five

2 20s 3 tens 5 ones

2 20s 2 tens 3 fives

2 20s 2 tens 2 fives 5 ones

2 20s 2 tens 1 five 10 ones

2 20s 2 tens 15 ones

2 20s 1 ten 5 fives

2 20s 1 ten 4 fives 5 ones

2 20s 1 ten 3 fives 10 ones

2 20s 1 ten 2 fives 15 ones

2 20s 1 ten 1 five 20 ones

2 20s 1 ten 25 ones

2 20s 7 fives

2 20s 6 fives 5 ones

2 20s 5 fives 10 ones

2 20s 4 fives 15 ones

2 20s 3 fives 20 ones

2 20s 2 fives 25 ones

2 20s 1 five 30 ones

2 20s 35 ones

with 2 20's there are 20 total ways

with either 2 or 3 20's there are 26 total ways

then calculate with 1 20 and no 20s, add them to 26

= 202