Substitute the definition \(\displaystyle ^nP_r\) and simplify. Then solve the resulting simple linear equation for n. Note that (n - 7)! = (n - 7)(n - 8)!

Link2: \(\displaystyle ^nP_6 = 90 \cdot ^nP_4\).

Done in a similar way. Yiou will end up with a quadratic equation to solve. Note that one of the solutions to this quadratic equation is not be valid.