0.8+0.2= 1, and the preceding c is a combination symbol. Therefore, the whole formula satisfies the binomial distribution of p = 0.8 and q = 1-0.8 = 0.2.

So the whole equation can be transformed into

44! /(n！ *(44-n)！ )*0.8^n*0.2^(44-n)

We can also find that 0.8/0.2=4.

So every time n increases 1, the second half of 0.8 n * 0.2 (44-n) becomes 0.8 (n+ 1) * 0.2 (43-n), which is equivalent to one more 0.8 and one less 0.2, which is four times of the original.

But the front part, 44! /(n！ *(44-n)！ ), with the increase of n 1, except for one more n+ 1 and one less 43-n, the whole becomes the original 43-n/n+ 1.

So when the whole result is maximum, we only need to solve n+ 1/(44-n)=4, and n=35. Of course, the actual 36 is also acceptable.

The maximum n is 35 and 36, both about 0. 147.

Another simple method is to use binomial mean * * *, that is, mean =n*p, n=44, p=0.8.

So the average value is 44 * 0.8 = 35,2, which is exactly between 35 and 36.