Question

2.
Find the unknown value
(1) nc2=28
find n?​

Answer 1

Step-by-step explanation:

nCr = n! / r! (n-r)!

nC2 = n (n-1) (n-2)!/2! ((n-2)!

28 = n(n - 1)/2

On solving we get n = 8

Answer 2

Given,

ⁿC₂ = 28

To find,

The value of n.

Solution,

The value of n is 8.

We can simply solve the mathematical problem by the following procedure.

We know by permutation and combination that,

∴ ⁿCₐ = $\frac{n!}{a!(n-a)!}$

Now,

It is given that,

⇒ ⁿC₂ = 28

By Permutation and Combination;

⇒ $\frac{n!}{2!(n-2)!}$ = 28

⇒ $\frac{1.2.3.4...n}{2* (1.2.3....(n-2))}$ = 28

⇒ (n-1) n = 28 x 2

⇒ n² - n - 56 = 0

By factorizing,

⇒ n² + 7n - 8n - 56 = 0

⇒ n(n+7) - 8(n+7) = 0

⇒ (n-8)(n+7) = 0

⇒ n = -7 or 8

Now,

The value of n cannot be negative.

Thus,

The value of n is 8.