Re: In how many different ways can pennies (1 cent), nickels (5 cents), di

On the first attempt, I made a guess and got it wrong.

Tried to solve it a few times and it still took me long but here's my approach:

1.10 - 0.41 = 0.69

I got 0.41 from adding each type of coin which is used at least once.

It is obvious that four pennies will be used and we have 0.65 to account for.

0.65 can have zero, one, two quarters.
65 = p + 5n + 10d + 25q

For zero quarters,
i. with zero dimes, there are fourteen ways to pick nickels and pennies.
65 = p + 5n (tried n for the range of 13 to 0)
ii. One dime, 12 ways to pick N and P.
iii. Two dimes, ten ways.
iv. Three dimes, 8 ways.
v. Four dimes, 6 ways,
vi. Five dimes, 4 ways.
vii. Six dimes, 2 ways.
So, zero quarters => 14 + 12 + 10 + 8 + 6 + 4 + 2 = 56 ways

Similarly, for One quarter,
Zero dimes (9 ways), One dime (7 ways), Two dimes (5 ways).....
9 + 7 + 5 + 3 + 1 = 25 ways

For Two quarters,
4 + 2 = 6 ways

Total : 56 + 25 + 6 = 87 ways.