Question

There are $12$ tube lights in a function hall.In how many ways can we illuminate the hall if even one tube light is enough for that purpose.

• A. $12$
• B. $2^{12}-1$
• C. $2^{12}$
• D. $12!$

Answer 1

Answer: (B)

$2^{12}-1$

Given that there are $12$ tube lights and only $1$ is enough to illuminate.

We can use $1,2,3,........12$ tube lights

We can choose this in ${}^{12}{C}_1,{}^{12}{C}_2......{}^{12}{C}_{12}$ ways

Total $={}^{12}{C}_1,{}^{12}{C}_2{}^{12}{C}_3+......{}^{12}{C}_{12}+({}^{12}{C}_0-{}^{12}{C}_0)$

$\Rightarrow 2^{12}-{}^{12}{C}_0=2^{12}-1$

Hence, the answer is $2^{12}-1.$