A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to
${2^{n - 1}}$
${2^n}$
${2^{n + 1}}$
${2^{2n}}$
Team $'A'$ consists of $7$ boys and $n$ girls and Team $'B'$ has $4$ boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to
The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is
On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is
If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^n{C_{r - 1}}$$ + {\,^n}{C_r} = $
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 $.........$.