Basic Counting Principles

Sum Rule Principle

Suppose that an event E can occur in m ways and a second event F can occur in n ways and suppose both events cannot occur simultaneously. Then E or F can occur in m+n ways.

Example – If 5 male professors and 8 female professors teach Maths then the students can choose a professor in 5+8 = 13 ways.

Product Rule Principle

Suppose that an event E can occur in m ways and a second event F independently can occur in n ways, then the combination of E and F can occur in mn ways.

Example – There are 8 boys and 5 girls in a classroom. If a boy and a girl chose for class monitor then students can choose the class monitor in 8×5 = 40 ways.

Factorial Function

The product of the first n natural number is called factorial n. It is denoted by n! read “n factorial”.

The factorial can also be written like this:
n! = n (n-1) (n-2) (n-3) …. 1.

0! = 1

Example: Find the value of 6!

Solution: 6! = 6 (6-1) (6-2) (6-3) (6-4) (6-5) = 6 x 5 x 4 x 3 x 2 x 1 = 720

Binomial Coefficients

Binomial Coefficients are denoted by nCr where r and n are positive integers, with r ≤ n.

Example: $${ 8_{C_{2}} = {8! \over 2!6!}} = {{8\times7\times6} \over {2\times6}} = 28$$

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