A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-
$2^{n-1}$
$2^{n+1}$
$2^{2n}$
$2^n$
How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels
If ${ }^{n} P_{r}={ }^{n} P_{r+1}$ and ${ }^{n} C_{r}={ }^{n} C_{r-1}$, then the value of $r$ is equal to:
The number of $4-$letter words, with or without meaning, each consisting of $2$ vowels and $2$ consonants, which can be formed from the letters of the word $UNIVERSE$ without repetition is $.........$.
A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?
In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?