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Answer

↓Steps Explained:↓

Evaluate the combination:

₇C₅

Combination Definition:

A unique order or arrangement

Combination Formula:

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

Plug in n = 7 and r = 5

Factorial Formula:

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

Calculate the numerator n!:

n! = 7!

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

7! = 5,040

Calculate (n - r)!:

(n - r)! = (7 - 5)!

(7 - 5)! = 2!

2! = 2 x 1

2! = 2

Calculate r!:

r! = 5!

5! = 5 x 4 x 3 x 2 x 1

5! = 120

Calculate ₇C₅

Final Answer