Factorial Manipulation

Problem Level: 2

51!/ 47!

Solution:

For those of you that do not know what the exclamation mark is, it is factorial.

It means to multiply the positive integers until 1.  It is assumed that 0! =1.

5! = 5 x 4 x 3 x 2 x 1 = 20 x 6 =120

6!= 720

10 ! = Well, forget it.

How would we find 51! Then?

Notice that 51! = 51 x 50 x 49 x 48 x 47 x 46! and 47! = 47 x 46!

Because both the numerator and the denominator have 47 x 46!, we can cancel it out. That leaves us with 51 x 50 x 49 x 48 which can be easily (not) calculated into 5997600.

Using this clever manipulation, you can change a once thought hard math problem into something manageable.