There are n distinct points on the circumfere | vedclass

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

Question

(B) To form a pentagon,we need to select $5$ points out of $n$ distinct points. The number of ways to do this is given by the combination formula $^nC

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) To form a pentagon,we need to select $5$ points out of $n$ distinct points. The number of ways to do this is given by the combination formula $^nC_5$.Similarly,to form a triangle,we need to select $3$ points out of $n$ distinct points. The number of ways to do this is given by $^nC_3$.According to the problem,the number of pentagons is equal to the number of triangles:$^nC_5 = ^nC_3$Using the property of combinations,if $^nC_r = ^nC_k$,then either $r = k$ or $n = r + k$.Since $5 
eq 3$,we must have $n = 5 + 3 = 8$.Therefore,the value of $n$ is $8$.

There are $n$ distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then the value of $n$ is

Similar Questions

The number of words that can be formed using the letters of the word $ARTICLE$,such that the vowels occupy even places,is

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

How many numbers lying between $500$ and $600$ can be formed with the help of the digits $1, 2, 3, 4, 5, 6$ when the digits are not to be repeated?

In how many different ways can the letters of the word $TABLE$ be arranged?

$A$ committee of $11$ members is to be formed from $8$ men and $5$ women. If $m$ is the number of ways to form the committee with at least $6$ men and $n$ is the number of ways to form the committee with at least $3$ women,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module