$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

In an examination,a question paper consists of $12$ questions divided into two parts,i.e.,Part $I$ and Part $II$,containing $5$ and $7$ questions,respectively. $A$ student is required to attempt $8$ questions in all,selecting at least $3$ from each part. In how many ways can a student select the questions?

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

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?

The number of ways to select $n$ objects from $2n$ objects, of which $n$ are identical and the rest are different, is:

The number of non-negative integral solutions of $x_1+x_2+x_3+x_4=10$ is