Question 38
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 $a+b(15-b)$.
$$
\binom{3003}{1},\binom{3003}{3002},\binom{a}{2},\binom{a}{a-2},\binom{15}{b},\binom{15}{15-b},\binom{14}{6},\binom{14}{8}
$$
Compute $a+b(15-b)$.