If $'n'$ objects are arranged in a row then the number of ways of selecting three of these objects so that no two of them are next to each othe
${}^{n - 2}{C_3}$
${}^{n - 2}{C_2}$
${}^{n - 3}{C_3}$
None
The number of matrices of order $3 \times 3$, whose entries are either $0$ or $1$ and the sum of all the entries is a prime number, is$....$
If $^n{P_r} = 840,{\,^n}{C_r} = 35,$ then $n$ is equal to
A boy needs to select five courses from $12$ available courses, out of which $5$ courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is
If $^{{n^2} - n}{C_2}{ = ^{{n^2} - n}}{C_{10}}$, then $n = $
Each of the $10$ letters $A,H,I,M,O,T,U,V,W$ and $X$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letters computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?