In a conference of $8$ persons, if each person shake hand with the other one only, then the total number of shake hands shall be
$64$
$56$
$49$
$28$
A bag contains $5$ black and $6$ red balls. Determine the number of ways in which $2$ black and $3$ red balls can be selected.
From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
A student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first five question. The number of choices available to him is
The number of onto functions $f$ from $\{1, 2, 3, …, 20\}$ only $\{1, 2, 3, …, 20\}$ such that $f(k)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is
In the $13$ cricket players $4$ are bowlers, then how many ways can form a cricket team of $11$ players in which at least $2$ bowlers included