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 can a student choose a programme of $5$ courses if $9$ courses are available and $2$ specific courses are compulsory for every student?
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 $.........$.
Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-