Question

If $12$ persons are seated in a row, the number of ways of selecting $3$ persons from them, so that no two of them are seated next to each other is

• A. $85$
• B. $100$
• C. $120$
• D. $240$

Answer 1

The correct option is C

$120$

Explanation for correct option:

Finding the possibilities:

Given, total $12$ persons are seated in a row.

The number of ways for selecting $3$ persons from $12$ people under the given data.

The Number of ways of arranging $3$ people from $9$ people seated in a row, in such a way that no two of them are consecutive.

$=$ Number of ways of arranging $3$ places from $10$

$=$${}^{10}C_3$

$=\frac{10!}{\left(10-3\right)!3!}$

$=\frac{10\times 9\times 8\times 7!}{7!\times 1\times 2\times 3}$

$=120$

Hence, correct answer is option $\left(C\right)$