Question

What is fundamental counting principle? What is the meaning of ${}^n{P}_r$?

Answer 1

Solution:

Fundamental principle of counting:

(i) Multiplication Principle: If an operation can be performed in ${}^{\prime }{m}^{\prime }$ different ways; following which a second operation can be performed in ${}^{\prime }{n}^{\prime }$ different ways, then the two operations in succession can be performed in $m\times n$ ways. This can be extended to any finite number of operations.

(ii) Addition Principle:If an operation can be performed in ${}^{\prime }{m}^{\prime }$ different ways and another operation, which is independent of the first operation, can be performed in ${}^{\prime }{n}^{\prime }$ different ways. Then either of the two operations can be performed in $(m+n)$ ways. This can be extended to any finite number of mutually exclusive operations.

Meaning of ${}^n{P}_r:$

The number of permutations of $n$ different things, taking $r$ at a time is denoted by ${}^n{P}_r.$