Question

On a new year's day every member of a family sends a card to every other member and the postman delivers 156 cards, the number of members of the family is:

• A. $12$
• B. $11$
• C. $14$
• D. $13$

Answer 1

The correct option is D $13$

We select 2 members(Let A and B) from the family and they Send 2 letters (A sends to B and B sends to A) So Number of Letters$=2{\times }^n{C}_2=n(n-1)$

Number of letters$=156$

So $n(n-1)=156$

$\Rightarrow n=13$