(B) The total number of ways to select $2$ students out of $20$ is given by $^{20}C_2$.Since each pair of students exchanges cards with each other,eac

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The total number of ways to select $2$ students out of $20$ is given by $^{20}C_2$.Since each pair of students exchanges cards with each other,each selection of $2$ students results in $2$ greeting cards being exchanged (one from student $A$ to $B$ and one from student $B$ to $A$).Therefore,the total number of greeting cards exchanged is $2 \times ^{20}C_2$.This is equivalent to $^{20}P_2$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Easy

On the occasion of the Deepawali festival,each student of a class sends greeting cards to every other student. If there are $20$ students in the class,then the total number of greeting cards exchanged by the students is:

A
$^{20}C_2$
B
$2 \times ^{20}C_2$
C
$^{20}P_2$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

Subtopic

Definition of permutation, Number of permutations with or without repetition, Conditional permutations

The number of words,with or without meaning,that can be formed by taking $4$ letters at a time from the letters of the word $'SYLLABUS'$ such that two letters are distinct and two letters are alike,is

MediumJEE MAIN 2020

View Solution

The number of natural numbers less than $1000$ in which no digit is repeated is

MediumTS EAMCET 2018

View Solution

Find the number of different $8$-letter arrangements that can be made from the letters of the word $DAUGHTER$ such that all vowels do not occur together.

Easy

View Solution

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

DifficultAP EAMCET 2001

View Solution

If the letters of the word $MOTHER$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $MOTHER$?

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

On the occasion of the Deepawali festival,each student of a class sends greeting cards to every other student. If there are $20$ students in the class,then the total number of greeting cards exchanged by the students is:

Similar Questions

The number of words,with or without meaning,that can be formed by taking $4$ letters at a time from the letters of the word $'SYLLABUS'$ such that two letters are distinct and two letters are alike,is

The number of natural numbers less than $1000$ in which no digit is repeated is

Find the number of different $8$-letter arrangements that can be made from the letters of the word $DAUGHTER$ such that all vowels do not occur together.

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

If the letters of the word $MOTHER$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $MOTHER$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module