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Let denote the number of triangles which can be formed by using the vertices of a regular polygon of sides. If , then equals
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Correct option is B
The number of triangles that can be formed by using the vertices of a regular polygon is nC3. That is Tn=nC3Now, Tn+1−Tn=21⇒ n+1C3−nC3=21⇒nC2+nC3−nC3=21 ∵n+1Cr=nCr−1+nCr⇒ 12n(n−1)=21 ⇒ n=−6 or 7As n is a positive integer, n = 7.Similar Questions
is equal to
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