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. $2\times {}^8{C}_3$
• B. $2\times {}^8{C}_4$
• C. ${}^8{C}_3$
• D. ${}^8{C}_4$

Answer 1

The correct option is A $2\times {}^8{C}_3$

​The number of ways of inviting, with the couple not included, is ${}^8{C}_5$.
The number of ways of inviting with the couple included, is ${}^8{C}_3$.

Therefore the required number of ways is
${}^8{C}_5+{}^8{C}_3={}^8{C}_3+{}^8{C}_3(\because {}^8{C}_5={}^8{C}_3)=2\times {}^8{C}_3$