Question

What is counting principle? Explain with uses.

Answer 1

Counting principle and it's uses:

In mathematics, we sometimes come across with a concept known as the ‘counting principle’. This is concerned with the total number of combinations. When we deal with the happening of two or more activities or events, it is often required to know quickly the number of total possible activities or events. It can be done by counting principle. This principle belongs to the topic ‘permutations and combinations’ from algebra – a branch of mathematics.

• Counting principle is quite commonly used in problems related to combination.
• The basic idea of counting principle is that if there’s particular number of ways of performing one action and some number of ways of performing another action, then total number of performing both actions would be equal to the product of both types of ways.
• The counting principle is also known as fundamental principle of counting or multiplication principle or rule of product. This principle is also used in probability theory and in number theory.

For example:Suppose you have $3$ shirts (call them $\text{A}$ , $\text{B}$ , and $\text{C}$ ), and $4$ pairs of pants (call them $w$ , $x$ , $y$ , and $z$ ). Then you have

$3\times 4=12$

Possible outfits:

$$\begin{gathered} Aw,Ax,Ay,Az \\ Bw,Bx,By,Bz \\ Cw,Cx,Cy,Cz \end{gathered}$$