Question

Ramya gives a dinner party for $5$ guests. The number of ways in which they maybe selected from among $9$ friends if two of the friends will not attend the party together is

• A. $84$
• B. $133$
• C. $91$
• D. $126$

Answer 1

The correct option is C $91$

Types of selection $\to$ No selecting any of those has $-1^{st}$ case

$\to$ select only one of the two $-2^{nd}$ case

For $1^{st}$ case no of ways ${=}^7{C}_5$

$(\because$ remaining are 7)

For $2^{nd}$ case no of ways ${=}^7{C}_4{\times }^2{C}_1=$

4 for remaining

So Total ${=}^7{C}_5{+}^7{C}_4{\times }^2{C}_1$

$=21+70=91$