Question

In 2nC2 + nC2 = 55 find n.​

Answer 1

Answer:

5

Step-by-step explanation:

2nC2 + nC2 = 55

Solve both separately first

2nC₂ = 2n!/2!(2n-2)!

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

          = 2n(2n-1)/2 = 2n(2n-1)/2 ------------------------ [1]

nC₂ = n!/2!(n-2)!

        = n(n-1)(n-2)!/2*1*(n-2)!

          = n(n-1)/2

Now substitute the values back.

=> 2n(2n-1)/2 + n(n-1)/2 = 55

=> 4n² - 2n + n² - n = 110

=> 5n² - 3n - 110 = 0

=> 5n² - 25n+22n - 110 = 0

=> 5n(n-5) + 22(n-5) = 0

=> (n-5)(5n+2) = 0

=> n = 5 or n = -2/5,

Since n cannot be negative thus n = 5