Question

Find the value of n and r when n+rP2=110 and n-rP2=20 .​

Answer 1

Answer:

Step-by-step explanation:

n=8,r=3

Answer 2

Answer: n = 8, r = 3.

Step-by-step explanation:

[ nPr = $\frac{n !}{(n - r) !}$  ]

Given, n+rP2 = 110

           n-rP2 = 20

So, n+rP2 = 110 = 11P2

      ∴ n + r = 11  ...(i)

Similarly, n-rP2 = 20 = 5P2

              ∴ n - r = 5 ...(ii)

Solving eq. (i) and (ii) to get the value of n and r :

  n + r = 11

+ n - r = 5  

 2n  = 16  

∴ n = 8

n + r = 11

∴ r = 11 - n

    =  11 - 8

    = 3

∴ The value of n is 8, and r is 3.