If P(n-1,3):P(n,3)=1:9 , find n ..
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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) = $\displaystyle \frac{n!}{(n-3)!}$ P(n-1,3) = $\displaystyle \frac{(n-1)!}{(n-4)!}$ and thus we have P(n-1,3):P(n,3) = n:n-3.... Can you continue ?
My attempt : After simplifying , i got $\displaystyle \frac{(n-1)(n-2)(n-3)}{n(n-1)(n-2)}=\frac{1}{9}$ $\displaystyle \frac{n-3}{n}=\frac{1}{9}$ $\displaystyle 9n-27=n$ n=27/8 ---- my answer is wrong .. Can someone pls spot my mistake . THanks .
Originally Posted by mathaddict My attempt : After simplifying , i got $\displaystyle \frac{(n-1)(n-2)(n-3)}{n(n-1)(n-2)}=\frac{1}{9}$ $\displaystyle \frac{n-3}{n}=\frac{1}{9}$ $\displaystyle 9n-27=n$ 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?
Well , let me retype the question . $\displaystyle P(n-1,3):P(n,3)=1:9$ , find n . The choices are (a) 6 (b) 7 (c) 8 (d) 9 (e) 4
Originally Posted by mathaddict Well , let me retype the question . $\displaystyle P(n-1,3):P(n,3)=1:9$ , 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 ....?
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