1. ## pleasehelp. permutations and combinations

The number of arrangements of 2n+2 different objects taken n at a time is to the number of arrangments of 2n different objects taken n at a time as 14:5. Find the value of n.

If 2nPn = 8.(2n-1)P(n-1), find the value of n

the P refers to the formula in permutations and combinations that is nPr = n!/(n-r)!

i dont understand how to solve these questions. some help is greatly appreciated. thankyou =D

2. Hello, flyinhigh123!

You're expected to know the formula for Permutations
. . and be able to handle factorials.

(1) The ratio of the number of arrangements of $2n+2$ different objects taken $n$ at a time
to the number of arrangments of $2n$ different objects taken $n$ at a time is $14:5$.
Find the value of $n$.
$2n+2$ objects taken $n$ at a time: . $_{2n+2}P_n \:=\:\frac{(2n+2)!}{(n+2)!}$

$2n$ objects taken $n$ at a time: . $_{2n}P_n \:=\:\frac{(2n)!}{n!}$

The ratio is: . $R \;=\;\frac{\dfrac{(2n+2)!}{(n+2)!}} {\dfrac{(2n)!}{n!}} \;=\;\frac{(2n+2)!}{(n+2)!}\cdot\frac{n!}{(2n)!} \;=\;\frac{(2n+2)!}{(2n)!}\cdot\frac{n!}{(n+2)!}$

And we have: . $\frac{(2n+2)(2n+1)}{(n+2)(n+1)} \;=\;\frac{14}{5} \quad\Rightarrow\quad 5(2n+2)(2n+1) \;=\;14(n+2)(n+1)$

. . which simplifies to: . $n^2 - 2n - 3 \:=\:0 \quad\Rightarrow\quad (n+1)(n-3) \:=\:0 \quad\Rightarrow\quad n \:=\:-1,3$

Therefore: . $\boxed{n \:=\:3}$

3. thankyou for your help soroban =D i realli appreciate your clear explaining and solution