# Thread: ratio

1. ## ratio

If P(n-1,3):P(n,3)=1:9 , find n ..

2. Originally Posted by mathaddict
If P(n-1,3):P(n,3)=1:9 , find n ..
Have you tried applying the definition of P(n,k)?

P(n,3) = $\frac{n!}{(n-3)!}$
P(n-1,3) = $\frac{(n-1)!}{(n-4)!}$

and thus we have P(n-1,3):P(n,3) = n:n-3....

Can you continue ?

3. ## Re :

My attempt :

After simplifying , i got

$\frac{(n-1)(n-2)(n-3)}{n(n-1)(n-2)}=\frac{1}{9}$

$\frac{n-3}{n}=\frac{1}{9}$

$9n-27=n$

n=27/8 ---- my answer is wrong .. Can someone pls spot my mistake . THanks .

4. Originally Posted by mathaddict
My attempt :

After simplifying , i got

$\frac{(n-1)(n-2)(n-3)}{n(n-1)(n-2)}=\frac{1}{9}$

$\frac{n-3}{n}=\frac{1}{9}$

$9n-27=n$

n=27/8 ---- my answer is wrong .. Can someone pls spot my mistake . THanks .
I'm sure n is meant to be a positive integer. It looks to me like the question has a typo in it. What answer does the book give?

5. ## Re :

Well , let me retype the question .

$P(n-1,3):P(n,3)=1:9$ , find n .

The choices are

(a) 6
(b) 7
(c) 8
(d) 9
(e) 4

6. Originally Posted by mathaddict
Well , let me retype the question .

$P(n-1,3):P(n,3)=1:9$ , find n .

The choices are

(a) 6
(b) 7
(c) 8
(d) 9
(e) 4
I meant a typo in the book (or wherever the question came from), not a typo in how you typed it. Test each option - do any of them work ....?