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Answer

↓Steps Explained:↓

Evaluate the combination:

₁₀C₂

Combination Definition:

A unique order or arrangement

Combination Formula:

where n is the number of items
r is the unique arrangements.

Plug in n = 10 and r = 2

Factorial Formula:

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

Calculate the numerator n!:

n! = 10!

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

10! = 3,628,800

Calculate (n - r)!:

(n - r)! = (10 - 2)!

(10 - 2)! = 8!

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

8! = 40,320

Calculate r!:

r! = 2!

2! = 2 x 1

2! = 2

Calculate ₁₀C₂

Final Answer