Permutations & Combinations Question (1 Viewer)

[Glen88]

Need some help with this.

If ²ⁿP_n = 8. ^2n-1P_n-1 , Find the Value of n.

 

[SoulSearcher]

Need some help with this.

If ²ⁿP_n = 8. ^2n-1P_n-1 , Find the Value of n.

²ⁿP_n = 8. ^2n-1P_n-1
i.e. (2n)!/(2n-n)! = 8 * (2n-1)!/[2n-1-(n-1)]!
(2n!)/n! = 8 * (2n-1)!/n!
[(2n)! - 8(2n-1)!]/n! = 0
(2n)! - 8(2n-1)! = 0
2n(2n-1)! - 8(2n-1)! = 0
(2n-8)(2n-1)! = 0
2n - 8 = 0, as (2n-1)! cannot equal zero
2n = 8
n = 4

 

[Glen88]

²ⁿP_n = 8. ^2n-1P_n-1
i.e. (2n)!/(2n-n)! = 8 * (2n-1)!/[2n-1-(n-1)]!
(2n!)/n! = 8 * (2n-1)!/n!
[(2n)! - 8(2n-1)!]/n! = 0
(2n)! - 8(2n-1)! = 0
2n(2n-1)! - 8(2n-1)! = 0
(2n-8)(2n-1)! = 0
2n - 8 = 0, as (2n-1)! cannot equal zero
2n = 8
n = 4

Thanks.