Question

What is the total number of ways of selecting at least one ring from 2 sets of 10 different rings?

• A. $2^{10}\times 2^{10}\times 2$
• B. $2^{10}+2^{10}$
• C. $2^{20}+1$
• D. $2^{20}-1$

Answer 1

The correct option is D $2^{20}-1$

Number of ways of selecting 10 distinctly different rings of 1 set = $2^{10}$
Since there are 2 sets, total selections are $2^{10}\times 2^{10}=2^{20}$
Since at least 1 has to be selected, total ways $=2^{20}-1$