Question

If np3=n-1P3+3(7P2), then n=

Answer 1

Answer:

Please see the attachment

Answer 2

Given :   ⁿP₂ = ⁿ⁻¹P₃  + 3(⁷P₂)

To find  :  Value of n

Solution:

ⁿPₓ  =  n!/(n-x)!

ⁿP₃ =  n!/(n - 3)!

ⁿ⁻¹P₃ =  (n-1)!/(n - 4)!

⁷P₂  = 7!/5!  = 42

n!/(n - 3)!  = (n-1)!/(n - 4)!   + 3(42 )

=> n!/(n - 3)! -   (n-1)!/(n - 4)!    = 3(42 )

=> (n!   - (n-3)(n-1)!)/(n - 3)!   =  3(42 )

=>  (n(n-1)!   - (n-3)(n-1)!)/(n - 3)!   =  3(42 )

=> (n-1)! (n - n - 3) / (n - 3)!   =  3(42 )

=> (n-1)! 3 / (n - 3)!   =  3(42 )

=> (n-1)!  / (n - 3)!   =   (42 )

=> ⁿ⁻¹P₂ = ⁷P₂

=> n - 1 = 7

=> n = 8  

or

(n-1)!  / (n - 3)!   =   (42 )

=> (n - 1)(n-2)   = 42

=> n² - 3n + 2 = 42

=> n² - 3n - 40 = 0

=> n² - 8n + 5n - 40 =0

=> n(n - 8) + 5(n - 8) = 0

=> (n + 5)(n-8) = 0

=> n = -5  or n = 8

n = 8    

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