There are seven candidates for $3$ posts. In how many ways can the posts be filled?

$A$ question paper has $2$ parts,part $A$ and part $B$,each containing $10$ questions. If a student has to choose $8$ questions from part $A$ and $5$ questions from part $B$,in how many ways can the student choose the questions?

The number of ways in which $6$ distinct rings can be worn on the $4$ fingers of one hand is:

How many numbers greater than $24,000$ can be formed by using the digits $1, 2, 3, 4, 5$,when no digit is repeated?

Eleven books consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $