$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

In how many ways can $4$ balls be picked from $6$ black and $4$ green colored balls such that at least one black ball is selected?

The number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is: