Question

How many are in A or B or C?

Short answer

There are 64 in A or B or C.

$\mathrm{n}(\mathrm{A}\cup \mathrm{B}\cup \mathrm{C})=64$

Step-by-step solution

Step 1. Given information

 Step 2. Calculation

$$\begin{gathered} \mathrm{From}\mathrm{the}\mathrm{venn}\mathrm{diagram}: \\ \mathrm{n}\left(\mathrm{A}\right)=(15+3+5+2)=25 \\ \mathrm{n}\left(\mathrm{B}\right)=\left(10+3+5+2\right)=20 \\ \mathrm{n}\left(\mathrm{C}\right)=\left(15+2+5+2\right)=24 \\ \mathrm{n}(\mathrm{A}\cap \mathrm{B}\cap \mathrm{C})=5 \\ \mathrm{Using}\mathrm{the}\mathrm{formula}: \\ \mathrm{n}(\mathrm{A}\cup \mathrm{B}\cup \mathrm{C})=\mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)+\mathrm{n}\left(\mathrm{C}\right)-\mathrm{n}(\mathrm{A}\cap \mathrm{B}\cap \mathrm{C}) \\ \mathrm{n}(\mathrm{A}\cup \mathrm{B}\cup \mathrm{C})=25+20+24-5 \\ \mathrm{n}(\mathrm{A}\cup \mathrm{B}\cup \mathrm{C})=64 \end{gathered}$$