Question

if six times the number permutations of n things taken 3 at a time is equal to seven times the number of permutations of (n-1) things chosen 3 at a time, find n​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{6{\times}P(n,3)=7{\times}P((n-1),3)}$

$\underline{\textbf{To find:}}$

$\textsf{The value of n}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\boxed{\mathsf{P(n,r)=n(n-1)(n-2)\;.\;.\;.\;.\;.\;.\;.r\;.factors}}$

$\mathsf{Consider,}$

$\mathsf{6{\times}P(n,3)=7{\times}P((n-1),3)}$

$\mathsf{6{\times}n(n-1)(n-2)=7{\times}(n-1)(n-2)(n-3)}$

$\mathsf{6{\times}n=7{\times}(n-3)}$

$\mathsf{6\,n=7n-21}$

$\mathsf{7n-6n=21}$

$\implies\boxed{\mathsf{n=21}}$

$\underline{\textbf{Find more:}}$

P (7,x) = 840

P= Permutation

With solution pleas

https://brainly.in/question/37701173  

P(13,r)=156 permutation po

https://brainly.in/question/39652921  

If 16Pr-1 : 15Pr-1 = 16 : 7 then find r.

a) 10

b) 12

c) 7

d) 8​

https://brainly.in/question/30103175