Question

find the value of n if p(n-1,3)ratio p(n+1,3)=5ratio12


Permutations sum
Answer me please​

Answer 1

Answer:

As we know,

n

P

r

=

(n−r)!

n!

n−1

P

3

:

n+1

P

3

=5:12

⇒

(n−2)!

(n+1)!

(n−4)!

(n−1)!

=

12

5

⇒

(n+1)n(n−1)

(n−1)(n−2)(n−3)

=

12

5

⇒12(n−2)(n−3)=5(n+1)n

⇒7n

2

−65n+72=0⇒7n

2

−56n−9n+72=0

⇒7n(n−8)−9(n−8)=0⇒(n−8)(7n−9)=0⇒n=8.