Question

Q1.find n if n-1p3 :np4=1:9​

Answer 1

Step-by-step explanation:

Answer: n = 9

Step-by-step explanation:

We know that,

$^nP_r=\frac{(n)!}{(n-r)!}$

We have,

$\begin{gathered}^{n-1}P_3=\frac{(n-1)!}{(n-1-3)!}\\\;\\^{n-1}P_3=\frac{(n-1)!}{(n-4)!}\\\;\\^{n-1}P_3=\frac{(n-1)(n-2)(n-3)(n-4)!}{(n-4)!}\\\;\\^{n-1}P_3=(n-1)(n-2)(n-3)\end{gathered}$

Similarly,

$\begin{gathered}^nP_4=\frac{n!}{(n-4)!}\\\;\\^nP_4=\frac{n(n-1)(n-2)(n-3)(n-4)!}{(n-4)!}\\\;\\^nP_4=n(n-1)(n-2)(n-3)\end{gathered}$

Now Given that,

$\begin{gathered}\frac{^{n-1}P_3}{^nP_4}=\frac{1}{9}\\\;\\\frac{(n-1)(n-2)(n-3)}{n(n-1)(n-2)(n-3)}=\frac{1}{9}\\\;\\\frac{1}{n}=\frac{1}{9}\\\;\\n=9\end{gathered}$

Hence,

n = 9

Answer 2

Answer:

hence n=9

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