Likelihood function of coin toss in three cases I have the following problem:

Lets flip a coin where the probability of getting heads is $\theta$.
  Write down $\theta$'s likelihood function in the three following cases:
  
  
*
  
*Throw the coin $n$ times, getting a total of 6 heads.
  
*Throw the coin $n$ times, getting the result (heads, heads, heads, heads, heads, heads, tails, tails, ..., tails), i.e. the first 6 flips
  are heads and the rest $n-6$ are tails. 
  
*Keep throwing the coin until you get 6 heads. It is noted that this required $n$ flips total.
  

This is my attempt to solve this: 


*

*$L(\theta)= {{n}\choose{6}}\theta^6(1-\theta)^{n-6}\propto \theta^6(1-\theta)^{n-6}$

*$L(\theta)= \theta^6(1-\theta)^{n-6}$

*?

My question is: Are my 1-2 solutions correct and what is the answer to
  part 3.? Is it the same as solution to part 2. or not?


Your answers for parts $(1)$ and $(2)$ look good.

For part $(3)$, subtract the respective probabilities for $k\;$heads, where $0 \le k\le 5$, from $1$, hence
$$L(\theta) = 1 - \sum_{k=0}^5{\small{\binom{n}{k}}}\theta^k(1-\theta)^{n-k}$$
