Question

A woman has 11 close friends. Number of ways in which she can invite them to dinner if two particular of them are not on speaking terms and will not attend together is

• A. $\stackrel{11}{\underset{5}{C}}-\stackrel{9}{\underset{3}{C}}$
• B. $\stackrel{9}{\underset{5}{C}}-\stackrel{9}{\underset{4}{2C}}$
• C. $\stackrel{9}{\underset{4}{3C}}$
• D. $\stackrel{9}{\underset{4}{C}}$

Answer 1

The correct option is A $\stackrel{11}{\underset{5}{C}}-\stackrel{9}{\underset{3}{C}}$

Given that a women has $11$ close friends$.$

$\because$ All possible combos -combos with both fighting friends

$\Rightarrow$ All possibilities ${=}^{11}{C}_5=462$ ways$.$

Two friends are on fight${=}^9{C}_3{\ast }^2{C}_2=84$ ways$.$

$\Rightarrow 462-84=378$ ways$.$