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

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

The total number of permutations of the letters of the word "$BANANA$" is

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 $^{12}P_r = 1320$,then $r$ is equal to

The total number of $3$-digit numbers,whose sum of digits is $10$,is