make 45 cents in change

[sanju09]

In how many ways can one make 45 cents in change using only nickels, dimes, and quarters, when any coin can be used for any possible number of times?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

[tpr-becky]

While I am sure there is a formula I did this quickly through logic-

Can't have 2 Quarters because that is too much
so if you have on quarter you need to add $.20 -

you can do $.20 with 2 dimes, 1 dime with 2 nickels, or 4 nickels (3 ways)

Or you can use zero quarters you'd need 4 dimes and 1 nickel, 3 dimes and 3 nickels, 2 dimes and 5 nickels, 1 dime and 7 nickels or 0 dimes and 9 nickels (5 ways)

For a total of 8 ways.

My logic went - how many ways if I use a quarter, and how many ways if I don't use a quarter.

[pardeep_10sharma]

Great mam.u did in awsome manner..........U r so intelligent. Thanks for sharing ur super duper soln and keep on sharing in future too........

While I am sure there is a formula I did this quickly through logic-

Can't have 2 Quarters because that is too much
so if you have on quarter you need to add $.20 -

you can do $.20 with 2 dimes, 1 dime with 2 nickels, or 4 nickels (3 ways)

Or you can use zero quarters you'd need 4 dimes and 1 nickel, 3 dimes and 3 nickels, 2 dimes and 5 nickels, 1 dime and 7 nickels or 0 dimes and 9 nickels (5 ways)

For a total of 8 ways.

My logic went - how many ways if I use a quarter, and how many ways if I don't use a quarter.

[cager]

thanks. does anyone know the formula?
in case there are questions that have more combination's than this.