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

In a club election,the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote is $62$,then the number of candidates is:

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls,one in each box,could be placed such that a ball does not go to the box of its own colour is

To fill $12$ vacancies,there are $25$ candidates,of which $5$ are from the scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all,then the number of ways in which the selection can be made is:

In how many ways can the letters of the word '$ALGEBRA$' be arranged when both $A$ do not come together?

The number of integers greater than $6000$ that can be formed using the digits $3, 5, 6, 7,$ and $8$ without repetition is: