Question

On the occasion of New Year each student of a class sends greeting cards to the others. If there are 20 students in the class, then the total number of greeting cards exchanged by the students is ______.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

There must be 2 students to exchange a greeting card, one student to send card and the other student to receive the card.

These 2 students can be selected out of 20 students in ${}^{20}{C}_2$ ways.

Since two students can exchange cards each other in two ways,

The total number of greeting cards exchanged by the students = $2{\times }^{20}{C}_2$