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
$96$
$128$
$24$
$72$
Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.
A student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select one book is $63$, then the value of $n$ is
For $2 \le r \le n,\left( {\begin{array}{*{20}{c}}n\\r\end{array}} \right) + 2\,\left( \begin{array}{l}\,\,n\\r - 1\end{array} \right)$ $ + \left( {\begin{array}{*{20}{c}}n\\{r - 2}\end{array}} \right)$ is equal to
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
There are $15$ persons in a party and each person shake hand with another, then total number of hand shakes is