If $\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11$, then $n$ satisfies the equation
$n^2 + n - 110 =0$
$n^2 + 2n - 80 =0$
$n^2 +3n- 108=0$
$n^2 + 5n - 84 =0$
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 total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is
If ${ }^{n} P_{r}={ }^{n} P_{r+1}$ and ${ }^{n} C_{r}={ }^{n} C_{r-1}$, then the value of $r$ is equal to:
How many numbers of $6$ digits can be formed from the digits of the number $112233$
A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to