The number of positive integral solutions of $a \cdot b \cdot c = 30$ is

The number of functions $f$ from $\{1, 2, 3, \dots, 20\}$ to $\{1, 2, 3, \dots, 20\}$ such that $f(k)$ is a multiple of $3$ whenever $k$ is a multiple of $4$ is:

The set $S = \{1, 2, 3, \ldots, 12\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \emptyset$. The number of ways to partition $S$ is

There are $n$ distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then the value of $n$ is

$X, Y, Z$ are sets of all positive divisors of $10^{60}, 20^{50}$ and $30^{40}$ respectively. Find $n(X \cup Y \cup Z)$.

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $1$ particular player is to be excluded?