4/7 is correct. We have 21 coins in the jar, the probability of gettin a nickle is 7/21 the probability of getting a dime is 9/21. The probability of a dime or nickle is the sum of the dime and nickel probability or 16/21.
With me so far
If you get a silver on the first draw then there are 20 coins left. 5 pennies and 15 silver coins. The odds of getting a silver coin is now 15/20.
Multiply the 2 probabilities together and you have (16/21)* (15/20) and you will get (240/420) which should simplify to 4/7.
For this problem I would draw a tree diagram to see the solution, if you think it will help you, post back and I will post a tree diagram. Problems like this are much easier to see visually