Inspired By Nihar Mahajan

You should mention that the probability of a (or any) user liking their post is 0.5.

Cheers! xD

Crap!Made a silly mistake.BTW @Mehul Arora The value of b is ambiguous cause 4 and 245351 are also co-prime and similarly 8 and 245351 is also co-prime. Hence value of b can be 2,4,8............Please check it.

Here's an almost generalized form for getting the probability of atleast $x$ likes with $n$ followers, and the added facts that $0\leq x\leq n$ and the probability of the problem being liked by each follower is $0.5$ . The generalization is as follows:

Let $\mathcal{P}_{n,x}$ denote the required probability. Then,

$\mathcal{P}_{n,x}=1-\frac{\displaystyle\sum_{i=0}^{x-1}\binom{n}{i}}{\displaystyle\sum_{i=0}^n\binom{n}{i}}=1-\frac{\displaystyle\sum_{i=0}^{x-1}\binom{n}{i}}{2^n}$

Now, there is no closed form for the sum $\displaystyle\sum_{i=0}^{x-1}\binom{n}{i}$ . We just manually compute it for given $x$ .

Note: By convention, for $x=0$ , we have $\displaystyle\sum_{i=0}^{-1}\binom{n}{i}=0$

The idea behind this generalization is counting the number of $p-$ element (followers) subsets $(0\leq p\leq x)$ of the set of $n$ elements (set of all the followers) and then using the classical definition of probability along with method of finding probability by complement.

For the problem here, taking $n=700$ and $x=3$ gives us the following:

$\mathcal{P}_{700,3}=1-\frac{\binom{700}{0}+\binom{700}{1}+\binom{700}{2}}{2^{700}}=1-\frac{245351}{2^{700}}=\frac{2^{700}-245351}{2^{700}}$

The result follows from here.