Question

# What is the fundamental counting principle? What is the meaning of $P_{r}^{n}$.

Hint: Firstly write the two fundamental principles of counting then try to explain them separately using an example. In the second part write what you understand from $P_{r}^{n}.$

The fundamental principle of counting has two principles: Multiplication principle, addition principle.

i) Multiplication principle:
If an operation can be performed in ‘m’ different ways; following which a second operation can be performed in ‘n’ different ways, then the two operations in succession can be performed in $\left( m\times n \right)$ ways. This can be extended to a finite number of operations.

Meaning of $P_{r}^{n}$ :
The number of permutations of ‘n’ different things, taking ‘r’ at a time is denoted by $P_{r}^{n}.$