Question

P(n,6)=3P(n,5).find the value of n​

Answer 1

p(n+6)=3p(n+5)

pn+6p=3pn+15p

pn-3pn=15p-6p

2pn=9p

n=9p/2p

n=9/2

Answer 2

The value of n is 8.

Step-by-step explanation:

Given : P(n,6)=3P(n,5).

To find : The value of n​ ?

Solution :

The permutation formula is $P(n,r)=\frac{n!}{(n-r)!}$

$P(n,6)=\frac{n!}{(n-6)!}$

$P(n,5)=\frac{n!}{(n-5)!}$

Substitute,

$\frac{n!}{(n-6)!}=3(\frac{n!}{(n-5)!})$

$\frac{n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)!}{(n-6)!}=3(\frac{n(n-1)(n-2)(n-3)(n-4)(n-5)!}{(n-5)!})$

$n(n-1)(n-2)(n-3)(n-4)(n-5)=3n(n-1)(n-2)(n-3)(n-4)$

$n-5=3$

$n=3+5$

$n=8$

The value of n is 8.

#Learn more

If P( n-1,3 ) : P ( n,4 ) = 1 : 9. Find r. Using permutation

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