SOLUTION: there are 4 dimes, 3 nickels, and 2 quarters. In how many possible ways can the selection be made so that the value of the coins is at least 25 cents

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