How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number
$5{ \times ^8}{P_3}$
$5{ \times ^8}{C_3}$
$5\;!\;{ \times ^8}{P_3}$
$5\;!\;{ \times ^8}{C_3}$
How many chords can be drawn through $21$ points on a circle?
In an election the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways, then the number of candidates is
The solution set of $^{10}{C_{x - 1}} > 2\;.{\;^{10}}{C_x}$ is
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 :
There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit