two ways, you toss a head or a tail...
0....you are only throwing 1 coin!
10 ways.
If you toss a coin 8 times and there are 7 heads, then there must be one tail each time. So how many ways can we get one tail? It can occur first, such as THHHHHHH or second HTHHHHHH etc. There are 8 places to put the T so there are 8 ways to have 7 heads and 1 tail.
15
Here are two ways: You could make a table: . |H | T --------- H| 1 0 T| 0 0 The row across the top is the first toss. The column is the second toss. The one with both Heads is indicated with a 1. There is 1 chance out of the 4 possible outcomes, so 1/4 = 0.25 Mathematically: Chance of first coin Heads = 0.5, chance of 2nd coin heads = 0.5; then multiply the two probabilities together, since they both have to happen: (0.5)*(0.5) = 0.25
As written, no ways are possible.
5 over 2, i.e. the number of combinations of 2 elements from 5. To understand this you need to study a little bit of combinatorics (how to count combinations): you might want to start from the lectures on combinatorics at statlect.com.
8.
You think of each toss as having heads or tails, so there are two choices. If you toss the coin twice you have 4 choices HH, TT, HT and TH. The number of different coin tosses is 2n ordered tosses and n+1 unordered. For example in two tosses, 22=4 ordered tosses if HT is different than TH and if HT is the same as TH then we have 2+1=3 different possible tosses. So using this if we toss a coin 5 times and order does not matter, there are 6 different possibilities. These are HHHHH, TTTTT, HTTTT, HHTTT, HHHTT, HHHHT,HHHHH. If order matters, there are 25=32 different possible ways to toss a coin 5 times. For example, HHHHT is different than THHHH. I will not write them all out, but you can do it easily by starting with HHHHH and changing each H to a T then two H to T and then 3, etc.
There are 4 ways to get 3 heads and 1 tail for 4 coin flips. They are: THHH, HTHH, HHTH & HHHT.
3 ways, out of 12 possible outcomes.
2, there could only be two outcomes. Heads or tails As in any experiment you need to define a valid toss. So if you are examining the number of heads and tails you would limit the outcomes to these two states. However, in a real world experiment there may be a condition where the coin landed on a uneven surface and was tilted in some way. The number of tilted ways is infinite. You could also have the coin land on its edge which is unlikely but possible.