We will get the number of possible selections, and then subtract 
the number less than 25 cents.

We can choose the number of dimes 5 ways 0,1,2,3, or 4.
We can choose the number of nickels 4 ways 0,1,2, or 3.
We can choose the number of quarters 3 ways 0,1, or 2.

That's 5*4*3 = 60 selections.

Now we must subtract from the 60 the number of selections 
of coins that are less than 25 cents.  These will involve only
dimes and nickels.

To get a selection of coins worth less than 25 cents:

If we use no dimes, we can use 0,1,2, or all 3 nickels.
That's 4 selections less than 25 cents.  (That includes
the choice of NO coins at all, which is counted as a choice 
contained in the 60, which we must subtract!)

If we use exactly 1 dime, we can use 0,1, or 2 nickels.
That's 3 combinations less than 25 cents.

And there is 1 other selection less than 25 cents, 2 dimes 
and no nickels.

So that's 4+3+1 = 8 selections which we must subtract from the 60.

Answer: 60-8 = 52 selections of coins worth 25 cents or more.  

Edwin