Question

On the occasion of Deepawali festival each student of a class sends greeting cards to others. If there are 20 students in the class, what is the number of cards sent by students?
A. ${}^{20}{C_2}$
B. ${}^{20}{P_2}$
C. $2 \times {}^{20}{C_2}$
D. $2 \times {}^{20}{P_2}$

Answer 1

Hint: In this question we have to calculate the total number of greeting cards by using the concept that each student will send cards to others and make cards for each other except for himself. Use this fact to calculate the number of cards sent. To solve this problem, we will use permutations.

Complete step-by-step answer:
Given, Total number of students = 20
Each student will make 20 – 1 = 19 Greeting cards.
$ \Rightarrow $Total number of Greeting cards made $ = 20 \times 19 = 380$
On carefully observing 380 we can say that $380 = {}^{20}{P_2}$
as ${}^{20}{P_2} = \dfrac{{20!}}{{(20 - 2)!}} = 380$
Hence if there are 20 students in the class then total number of cards sent by the students $ = {}^{20}{P_2}$
$\therefore $ Option B. ${}^{20}{P_2}$ is the correct answer.

Note- For such types of questions if n students are there then use the formula to find the number of greeting cards sent by the students $ = n \times (n - 1)$ because a student will not send the card to himself/herself.