Solve For $n$ $$42 \cdot { } _ { n - 1 } P _ { 5 } = { } _ { n + 1 } P _ { 6 }$$

Solve for $n$ .
$$42 \cdot { } _ { n - 1 } P _ { 5 } = { } _ { n + 1 } P _ { 6 }$$

A) $n = 35$
B) $n = 7,34$
C) $n = 6,35$
D) $n = 6$
E) no solution