Question

There are $100$ different books in a shelf. Number of ways in which $3$ books can be selected so that no two of which are neighbours is?

• A. ${}^{100}{C}_3-98$
• B. ${}^{97}{C}_3$
• C. ${}^{96}{C}_3$
• D. ${}^{98}{C}_3$

Answer 1

The correct option is A ${}^{100}{C}_3-98$

No. of ways to select $=C_3^{100}$.

No. of $3$ consecutive points$=98$

So, Total no. of ways for required condition$=C_3^{100}-98$