Factorials

• Factorial of a number - the product of itself with all positive integers less than 1

  • n! = n × (n-1) × (n-2) …

  • ex; 2! = 2 × 1 = 2; 3! = 3 × 2 × 1 = 6; 4! = 4 × 3 × 2 × 1 = 24

  • 0! = 1

• Binomial coefficient - (n / k) = n! / k! (n-k)!

SOLVE 6! / 5!; 2 methods

1. 6 × 5 × 4 × 3 × 2 × 1 / 5 × 4 × 3 × 2 × 1 ; cancel out

   = 6

2. 6! / 5! = 720 / 120 = 6

              

SOLVE (6 / 2)

• 6! / 2! (6-2)!

  6! / 2! × 4!

  6 × 5 × 4 × 3 × 2 × 1 / 2 × 1 × 4 × 3 × 2 × 1; cancel out

  6 × 5 / 2 × 1

  30 / 2

  = 15

SOLVE (3 / 3)

• 3! / 3! (0)!

  3! / 3! × 1

  3! / 3!

  = 1