# Need help finding "n" in Permutations!

#### mr fantastic

MHF Hall of Fame

Please help me. I do not know how to solve for n. Thank you.
Link1: $$\displaystyle ^nP_8 = 13 \cdot ^nP_7$$.

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.

krzyrice

krzyrice

#### krzyrice

thank you so much for the help guys