Question

$20$ persons are setting in a particular arrangement around a circular table. Three persons are to be selected for leaders. The number of ways of selection of three persons such that no two were sitting adjacent to each other is

• A. 600
• B. 900
• C. 800
• D. None of these

Answer 1

Answer: (C)

Total ways of selection without restriction $={}^{20}{C}_3$
Number of ways of selection when two are adjacent
$=20\times {}^{16}{C}_1$
Number of ways of selection when all the three are adjacent $=20$.
Required number of ways $={}^{20}{C}_3-20\times 16-20$
$=\frac{20\times 19\times 18}{6}-20\times 16-20=20[57-16-1]$
$=20\times 40=800$