Standard deviation formula for multiple binomial distribution

Question

I want to combine more than 20 different binomial distributions and then I would like to find their combined standard deviation.

For the time being, let us assume that there are only $3$ different binomial distributions with the following parameters:

First:
$n = 1000$; $p = 2.5$%

Second:
$n = 400$; $p = 6$%

Third:
$n = 200$; $p = 3$%

I want to combine those $3$ into one case, how do I find the standard deviation of the combined case?

I do know the simple formula for just one binomial distribution is this:

$$\sqrt{n p (1-p)}$$

Answer 1

I have found the answer and it's actually very simple just $$\sqrt {\sum_{i=0}^k {n_i p_i ( 1 - p_i )}}$$

so the standard deviation of that three combined case above is $\sqrt {(1000 \times 2.5\% ( 1 - 2.5\% )) + (400 \times 6\% ( 1 - 6\% )) + (200 \times 3\% ( 1 - 3\% ))}$

$= 7.263263729$