Verify the following extension of the addition rule (a) by an appropriate Venn diagram and (b) by a formal argument using the axioms of probability and the propositions in this chapter. P(A B C) = P(A) + P(B) + P(C) P(A B) P(A C) P(B C) + P(A B C)

Lecture 10/04/2017 → Section 3.4 ← Factorial Factorials count the number of ways of order “n” objects without repetition, and is defined as, n! = n • (n - 1) • (n - 2) • … • 3 • 2 • 1 o 0! = 1 o Example: How many ways can someone rearrange 4 books on a shelf 4! = 4 • 3 • 2 • 1 = 24 ways o n! In terms of (n - 1)! n! = n • (n -1)! o In terms of (n - 2)! n! = n • (n - 1) • (n -2)! Permutations A ‘permutation’ is one of the different arrangements of a group of items where order matters. i.e., This gives the number of ways to arrange in order ‘n’ distinct objects taken ‘r’ at a time without repe