Stuck on this permutations and combinations problem. Can someone help! 
A coin is tossed $10$ times.
a) How many different sequences of heads and tails are possible?
b) How many different sequences containing $6$ heads and $4$ tails are possible?
c) What is the probability of getting $6$ heads and $4$ tails?

I genuinely just don't know what to do: I've tried $10!$ and $\binom{10}{2}$ but I'm clueless.
 A: Let's put the ideas in the comments together (particularly, the ones by @Peter). I'll begin by solving a similar problem:
finding the probability of getting exactly 3 Heads in five tosses of a fair
coin.
(a) Possible sequences: $2^5 - 32.$ There are two possibilities on each of five tosses.
Sample space $S$ can be represented as follows. There are $1 + 5 + 10 + 10 + 5 + 1 = 32$ elements in the sample space.
HHHHH
HHHHT HHHTH HHTHH HTHHH THHHH
HHHTT HHTHT HTHHT THHHT HHTTH HTTHH TTHHH HTHTH THTHH THHTH
TTTHH TTHTH THTTH HTTTH TTHHT THHTT HHTTT THTHT HTHTT HTTHT
TTTTH TTTHT TTHTT THTTT HTTTT
TTTTT

(b) Sequences with exactly three Heads: ${5 \choose 3} = 10.$
    There are five 'slots' to fill, choose three of them for Heads in
    ${5 \choose 3}$ ways, put Tails in the remaining two slots.
    These are the ten sample elements on the third row above.
HHHTT HHTHT HTHHT THHHT HHTTH HTTHH TTHHH HTHTH THTHH THHTH

(c) Probability of getting exactly three Heads in five tosses: 
${5 \choose 3}/2^5 = 10/32 =5/16.$
In a similar way, except that I don't have the patience to type the 1024
sample elements, the probability of getting exactly six heads in ten
tosses is ${10 \choose 6}/2^{10}.$
Addendum: If you haven't already seen it, your course should soon
cover the binomial distribution. The number $X$ of heads in $n = 10$ tosses
of a fair ($p = 1/2$) coin has a binomial distribution. Specifically,
$X \sim Binom(n = 10, p = 1/2).$ 
The formula for the PDF of a binomal distribution is
$$P(X = k) = {n \choose k}p^k(1-p)^{n-k},$$
for $k = 0, 1, \dots, n.$ In case $p = 1/2 = 1 - p,$ this formula simplifies to
$P(X = k) = {n \choose k}/2^n.$
Below is a bar graph of $Binom(10,1/2),$ in which the bar for $P(X = 6)$ is emphasized in a different color.

