Additional counting problems:

The following relationship governs the cardinality of sets:

card(AÈBÈC)= card A + card B + card C - card (AÇB) - card (AÇC) - card (BÇC) + card (AÇBÇC)

Use this relationship to solve these problems:

1. From a survey of 120 people, the following data were obtained:

90 owned a car
40 owned a home
35 owned a computer
32 owned a car and a home
21 owned home and a computer
26 owned a car and a computer
17 owned all three

a) How many people in this survey owned either a car, a home, or a computer?
b) How many people owned neither a car, nor a home, nor a computer?
c) How people owned only a computer?

2. Find the number of integers in the set {n: 100 £ n £ 999} with at least one kth digit equal to k for k = 1,2,3.

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