Question

There are $n$ different books having $m$ copies each. If the total number of ways of making at least one selection from them is $255$ and $m-n+1=0$, then distance of point $(m,n)$ from the origin is

• A. $3$
• B. $4$
• C. $5$
• D. None of these

Answer 1

Answer: (C)

$5$

$n$ different books with $m$ copies of each
Number of ways of selection $={(m+1)}^n-1$
$\Rightarrow (m+1{)}^n=256$

We know that $4^4=256$
Hence $n=4$

Now, $m-n+1=0$

$\Rightarrow m=3$
So, distance of $(3,4)$ from origin is $5$

Hence, option C.