Question

$15$ persons are sitting around a circular table. The number of ways of selecting three persons at a time from them, such that the selected three did not sit together at one place is

• A. 455
• B. 15
• C. 45
• D. 440

Answer 1

Answer: (D)

The total number of ways selecting 3 persons from 15 persons seat around a circular table is ${}^{15}{C}_3$
Now, number of ways selecting 3 persons who sit together at one place is 15 .
So, required number of ways $={}^{15}{C}_3-15$
$=\frac{15\times 14\times 13}{3\times 2}-15$
$=35\times 13-15$
$=455-15=440$