There are n distinct points on the circumfere | vedclass

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(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

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