Question

If N objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is

• A. $\frac{(n-2)(n-3)(n-4)}{6}$
• B. ${}^{n-2}{C}_3$
• C. ${}^{n-3}{C}_3{+}^{n-3}{C}_2$
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\frac{(n-2)(n-3)(n-4)}{6}$
B ${}^{n-2}{C}_3$
C ${}^{n-3}{C}_3{+}^{n-3}{C}_2$

Hence, Option(A,B,C) are the correct answers.