Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is
$^{52}{C_{26}}\;.\;{2^{26}}$
$^{104}{C_{26}}$
$2\;.{\;^{52}}{C_{26}}$
None of these
In how many ways $5$ speakers $S_1,S_2,S_3,S_4$ and $S_5$ can give speeches one after the other if $S_3$ wants to speak after $S_1$ & $S_2$
The least value of a natural number $n$ such that $\left(\frac{n-1}{5}\right)+\left(\frac{n-1}{6}\right) < \left(\frac{n}{7}\right)$, where $\left(\frac{n}{r}\right)=\frac{n !}{(n-r) ! r !}, i$
In a football championship, there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is
A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to