A coin is flipped $6$ times in a row.

a. What is the probability that it never lands heads up?

b. What is the probability that it lands heads up exactly $3$ times?

c. What is the probability that it lands heads up at most $3$ times?

**My attempt**

b) $p=\frac{1}{2}$

$q=p=\frac{1}{2}$

so, I got ${6\choose 3}(\frac{1}{2})^3(\frac{1}{2})^3$

c) $p=\frac{1}{2}$

$q=p=\frac{1}{2}$

so, I got $ {6\choose 3}(\frac{1}{2})^3(\frac{1}{2})^3\times{6\choose 2}(\frac{1}{2})^2(\frac{1}{2})^4\times{6\choose 1}(\frac{1}{2})^1(\frac{1}{2})^5$