The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is
$2252$
$2356$
$2162$
$2454$
Let $A=\left[a_{i j}\right], a_{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$. The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is $........$.
$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
Determine $n$ if
$^{2 n} C_{3}:\,^{n} C_{3}=12: 1$
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included