Combinatorics

Simplifying Factorials

Cancellation in (n+k)!/n!

  • High school
  • about 3 min
  • 3 of 11 in the family
Not started

Numerator: (4+2)! = 6!

654321

Denominator: 4!

4321
=6×5= 30
(4+2)!4!=6!4!=6×5=30\frac{(4+2)!}{4!} = \frac{6!}{4!} = 6\times5 = 30

(n+k)!/n! - denominator n! cancels the bottom 4 numbers. 2 numbers from 5 to 6 remain.

Where it is taught