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Factorial of a number \[n\] is defined as the product of all whole numbers from 1 up to \[n\],
\[n!=n(n-1)(n-2)(n-3).........1\] This special numerical concept is vital for calculating permutations and combinations, serving as a valuable analytical tool for problem-solving. Factorials are instrumental in revealing the various possible arrangements of objects, making them an essential component in mathematical and computational applications.

Combination \[C(n,k)\] formula, where \[ k \leq n\] is defined as
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!}\] The formula is typically expressed as \[^nC_k\]. In mathematics a combination refers to the act of selecting items from a set with distinct members, wherein the order of selection holds no significance. These selections are representative of the various ways objects can be chosen from a given set, with \[n\] denoting the total number of objects and \[k\] representing the specific number of objects chosen.

Permuation \[P(n,k)\] formula, where \[ k \leq n\] is defined as
\[ \binom{n}{k} = \frac{n!}{(n-k)!} \] The formula is typically expressed as \[^nP_k\]. It is a mathematical approach to find the quantity of potential arrangements within a specific set by taking into account the of order of selection (unlike combination). In this context, \[n\] represents the total count of objects under consideration, whereas \[k\] denotes the specific number of objects designated for selection.