Question

Kanchan has $10$ friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in which she can invite five friends is

• A. ${}^8{C}_5$
• B. $2{\times }^8{C}_5$
• C. ${}^{10}{C}_5-2{\times }^8{C}_4$
• D. None of these

Answer 1

Answer: (B)

$2{\times }^8{C}_5$

The number of ways of inviting, with the couple not included ${=}^8{C}_5$
The number of ways of inviting, with the couple included ${=}^8{C}_3$.
$\therefore$ The required number of ways
${=}^8{C}_5{+}^8{C}_3{=}^8{C}_5{+}^8{C}_5=2{\times }^8{C}_5\left[{\because }^8{C}_5{=}^8{C}_3\right]$