HMMT November 2020 U10

The number 3003 is the only number known to appear eight times in Pascal's triangle, at positions

$$\binom{3003}{1},\binom{3003}{3002},\binom{a}{2},\binom{a}{a-2},\binom{15}{b},\binom{15}{15-b},\binom{14}{6},\binom{14}{8}$$

Compute $a+b(15-b)$.