Q.Evaluate $\dfrac{7!}{5!\,2!}$.

The factorial of a whole number $n$, written $n!$, is the product of every whole number from $n$ down to $1$: $n! = n(n-1)(n-2)\cdots2\cdot1$. It is the building block of every permutation and combination formula. $0! = 1$ is a defined starting rule (an axiom), not something worked out by multiplying — it is fixed this way so that the boundary cases of $^{n}P_{r}$ and $^{n}C_{r}$ (like $^{n}P_{0}=1$) come out correctly. Factorials can be simplified quickly using $n! = n \times (n-1)!$, which lets a ratio like $\dfrac{7!}{5!}$ be evaluated as $7 \times 6 = 42$ without expanding either factorial fully.