Business Statistics

Chapter 5 | Probability 167

Similarly, in an experiment involving the tossing of six coins, the total possible outcomes are

(2) × (2) × (2) × (2) × (2) × (2) = 64

5.4.2 Counting Rules for Combinations

The second counting method uses the concept of combinations. Sampling of n items from a population

of size N (usually larger) without replacement provides

!

( , )

!( )!( )

= =

−

N

n

N

C C N n

N n n

where !N = (N) × (N–1) × (N – 2) ×

…

× (2) × (1)

!n = (n) × (n – 1) × (n – 2) ×

…

× (2) × (1)

and !0 = 1

The term factorial is represented by the symbol “!”. For example, !4 = 4 × 3 × 2 × 1 = 24. Example 5.1

specically explains the concept of counting rules ...