l 7 Combinations of 4

Enter n

Enter r

  

Evaluate the combination:

7C4

Combination Definition:

A unique order or arrangement

Combination Formula:

nCr  =  n!
  r!(n - r)!

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

Plug in n = 7 and r = 4

7C4  2  7!
  4!(7 - 4)!

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 - 4)!

(7 - 4)! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate r!:

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 7C4

7C4  =  5,040
  24 x 6

7C4  =  5,040
  144

Final Answer


7C4 = 35