Question

using a tree diagram that shows how many ways a nickel a dime and a quarter can be flipped determine how many ways you can get exactly one tail

Answer 1

Start with N (Nickel) at the top. Draw two arrows leading down-left and down-right. Let's have all of the down-left arrows represent "Heads" and all of the down-right arrows representing "Tails"

So, those arrows should each point to a D (Dime) (meaning, there will be 2 Ds). Again, since you have heads or tails, draw two arrows coming down from each of the D's.

Now, each of those arrows should point to a Q (Quarter) (meaning that there will be 4 Qs). Again, since you have heads or tails, draw two arrows coming down from each of the Qs.

You now have a tree showing all the possibilities. Now you are looking for all the instances where you have one down-right arrow (Tails) and two down-left arrows (Heads)

For instance:
N -(H)-> D -(H)-> Q -(T)->
Nickel = Heads
Dime = Heads
Quarter = Tails