On her vacations,Veena visits four cities $(A, B, C, D)$ in a random order. What is the probability that she visits $A$ just before $B$?

Number of $4-$digit numbers (the repetition of digits is allowed) which are made using the digits $1, 2, 3$ and $5$,and are divisible by $15$,is equal to $............$.

If $\sum\limits_{r = 0}^{25} {\left( {^{50}C_r \cdot ^{50 - r}C_{25 - r}} \right) = K\left( {^{50}C_{25}} \right)}$,then $K$ is equal to

The number of ways of selecting $8$ letters from $24$ letters,of which $8$ are $a$,$8$ are $b$,and the remaining $8$ are distinct,is given by:

Out of $6$ distinct novels and $3$ distinct dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf such that the dictionary is always in the middle. What is the number of such arrangements?

$2^n \{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 3) \cdot (2n - 1)\} = \dots$