Question

find n if 2.np3= n+1p3​

Answer 1

Given: The term 2(np3) = (n+1)p3

To find: The value of n?

Solution:

• Now we have given the term:

               2(np3) = (n+1)p3

• Expanding it, we get:

              2 x n(n-1)(n-2) = (n+1)(n)(n-1)

• Now cancelling common terms, we get:

              2 x (n-2) = (n+1)

              2n - 4 = n + 1

               n = 5

Answer:

           So the value of n is 5.

Answer 2

Given :  2. ⁿP₃  = ⁿ⁺¹P₃

To find : Value of n

Solution:

2. ⁿP₃  = ⁿ⁺¹P₃

ⁿPₓ  =  n!/(n-x)!

ⁿP₃ =  n!/(n - 3)!

ⁿ⁺¹P₃ = (n + 1)!/ (n+1 - 3)!  =  (n + 1)!/ (n - 2)!

2 *  n!/(n - 3)!     =  (n + 1)!/ (n - 2)!

=> 2 * n!/(n - 3)!  = (n+1).n! / (n - 2)(n- 3)!

=> 2  = (n + 1)/(n - 2)

=> 2n - 4  = n + 1

=> n = 5  

Verification

⁵P₃  =  5!/2! = 5 * 4 * 3 = 60

⁶P₃  = 6!/3! = 6 * 5 * 4 * = 120

120 = 2 * 60

=>  ⁶P₃   = 2 * ⁵P₃

ⁿ⁺¹P₃ = 2. ⁿP₃

n = 5

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