Question

A shopkeeper has $10$ copies each of nine different books, then the number of ways in which atleast one book can be selected is

• A. $9^{11}-1$
• B. $10^{10}-1$
• C. $11^{9}-1$
• D. $10^{9}$

Answer 1

Answer: (C)

$\underset{10}{\underset{︸}{B_{1}}} \underset{10}{\underset{︸}{B_{2}}} \underset{10}{\underset{︸}{B_{3}}} \ldots \ldots .. \underset{10}{\underset{︸}{B_{9}}}$
$1^{s t}$ kind of book can be selected in $\left(10 + 1\right)$ ways.
Similarly each kind of book can be selected in $\left(10 + 1\right)$ ways.
So, selection of atleast one book $=\left(10 + 1\right)\left(10 + 1\right)\ldots \ldots \ldots ..\left(10 + 1\right)\left(9 \, t i m e s\right)-1$
$=11^{9}-1$