The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is:

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken $3$ at a time without repetition and each arrangement containing at least one vowel,is

Ten persons,among whom are $A, B$,and $C$,are to speak at a function. The number of ways in which they can speak if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is:

How many words can be formed by using all the letters of the word '$TRIVANDRUM$' using each letter exactly once (in $!$)?

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

Assuming that no two consecutive digits are same,the number of $n$-digit numbers is: