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 words not starting and ending with vowels formed, using all the letters of the word $'UNIVERSITY'$ such that all vowels are in alphabetical order, is
In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman
Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to
If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals
The number of seven digit positive integers formed using the digits $1,2,3$ and $4$ only and sum of the digits equal to $12$ is $...........$.