Question

In how many ways can $3$ girls and $3$ boys be seated at round table,so that any $2$ and only $2$ of the girls are together?

• A. $72$
• B. $144$
• C. $36$
• D. $64$

Answer 1

Answer: (C)

$36$

$3$ Girls , $3$ Boys

Number of ways in which boys can be arranged $=(3-1)!=2!=2$ ways

Let $2$ girls be concidred as $1$ entity

Internal arrangements ${=}^3{C}_2(2!)=3(2!)=6$ Ways

Number of ways of placing them

$2\times 2!{\times }^3{C}_2{\times }^3{C}_2$

$=36$ Ways

Option : C