142. Counting Principle

Count the total number of possible outcomes in a multi-step process

then the total number of outcomes is:

Permutations

Number of -element subsets of a given -element set

Because :

Ordering elements
Ordering out of
Choosing and ordering out of
Number of subsets of
Sequences of length from choices
Example

Find the probability that 6 rolls of a fair 6-sided die all give different numbers

  • Total outcomes for 6 rolls:
  • Favorable outcomes (all numbers different):

Therefore:

Combination

Definition: Number of -element subsets of a given -element set

Two ways to construct an ordered sequence of distinct items: