Question

\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)

• A. \( 3 \)
• B. \( 6 \)
• C. \( 9 \)
• D. \( 12 \)

Hint:

Key identity: \( \binom{n+1}{r} - \binom{n}{r} = \binom{n}{r-1} \). For \( r=3 \), \( \binom{m+1}{3} - \binom{m}{3} = \binom{m}{2} \).

Answer 1

The Correct Option is B