Probability Theory

Any set of r elements chosen from a population of n elements, without regard for order, is called a subpopulation of size r of the original population. The number of such subpopulations is given by

THEOREM 1.3. A population of n elements has precisely

subpopulations of size r < n.

The number is sometimes called the number of combinations of n things taken r at a time (without regard for order).

Roughly speaking, the probability P(A) of the event A equals the fraction of experiments leading to the occurrence of A in a large series of trials.