Remember that a factorial (written with the "!" notation) means to multiply all the natural numbers (1, 2, 3,...) up to and including the number listed. So (4!)=1xx2xx3xx4(4!)=1×2×3×4
If I had (4!)/(3!)4!3!, that'd the same as
(4xx3xx2xx1)/(3xx2xx1)4×3×2×13×2×1. But we can also rewrite this as:
(4xx3!)/(3!)4×3!3! and so can cancel out the 3!3! and end up with 4.
In the above question, we have
(12!)/(8!4!)12!8!4! which I can rewrite as:
(12xx11xx10xx9xx8!)/(8!4!)12×11×10×9×8!8!4! and so can cancel the 8!8!:
(12xx11xx10xx9)/(4!)12×11×10×94! and if I expand the 4!4! we get:
(12xx11xx10xx9)/(4xx3xx2xx1)12×11×10×94×3×2×1 and we can cancel out some stuff:
(cancel(12)xx11xxcancel(10)color(red)(5)xx9)/(cancel(4xx3)xxcancel(2)xx1) and cleaning it up we have:
11xx5xx9=495
