Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1−Tn=10Tn+1−Tn=10, then the value of n is	Pick:	A) 5	B) 6	C) 7	D) 8	E) 10
We are given that Tn+1−Tn=C3n+1−C3n=10 --&gt; C3n+1−C3n=(n+1)!/3!(n−2)!−n!3!(n−3)!=10 --&gt; (n−1)n(n+1)/6−(n−2)(n−1)n/6=10 (n−1)n=20 --&gt; n=5n=5.   Answer: A.   Or: one additional point gives 10 more triangles, so when we add one point there are 10 different pairs of points which make triangles with that additional point --&gt; C2n=10--&gt; (n−1)n=20 --&gt; n=5   5nswer: 5.
<result>A</result>
Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1−Tn=10Tn+1−Tn=10, then the value of n is