Assume you are selecting three (3) coins; there are 5 dimes, 4 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?

Question

Assume you are selecting three (3) coins; there are 5 dimes, 4 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?

anonymous · Answer

can you help me with the values of dimes......

zarkon · Answer

dimes are 10 cents

anonymous · Answer

nickels=?
quarters=?

anonymous · Answer

nickles = 5 cents, quarters = 25 cents.

anonymous · Answer

here we cant get a sum of 25 only in two cases
3nickels     and      2nickels+1dimes  
so subtract these two selections from the total

anonymous · Answer

11c3-(4c2*5c1+4c3)=131

anonymous · Answer

is it correct?

zarkon · Answer

it is

zarkon · Answer

you can also count directly

$${2\choose 2}{9\choose 1}+{2\choose 1}{9\choose 2}+{2\choose 0}{5\choose 3}{4\choose 0}+{2\choose 0}{5\choose 2}{4\choose 1}$$

anonymous · Answer

first one may be easier

zarkon · Answer

it is ...and it is how i originally did it.  After you posted I decided I would  show another way that gives the same answer

anonymous · Answer

Yes that is correct.  Thank you both very much.