The number of non-negative integral solutions of the equation $x+y+z+t=10$ when $x \geq 2, z \geq 5$ is

The number of integers lying between 1000 and 10000 such that the sum of all the digits in each of those numbers becomes 30 is

If all the letters of the word MOST are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order, then the rank of the words STOM when counted from the rank of the word MOST, is

The constant term in the expansion of $\left(1+\frac{1}{x}\right)^{20}\left(30 x(1+x)^{29}+(1+x)^{30}\right)$ is