Evaluate. 5!4! = [?]

1 Answer

2880

Explanation:

#!# in mathematics means factorial.

What is factorial?

Factorial is the product of an integer and all below it to #1#

#n!##=n*(n-1)!# for #n≥1# or simply #n!##=1*2*3*...n#

Notice that #0!# is defined as #1# by mathematicians as it is the empty product.

So for #5!#, we have

#5!##=5*(5-1)!# #rArr5!##=5*4!#

#5!##=5*4*(4-1)!# #rArr5!##=5*4*3!#

#5!##=5*4*3*(3-1)!# #rArr5!##=5*4*3*2!#

#5!##=5*4*3*2*(2-1)!# #rArr51##=5*4*3*2*1!#

But, #1!##=1*(1-1)!#

Which is #1!##=1*0!# and #0!##=1#

Finally,

#rArr5!##=5*4*3*2*1#

That is the pattern, so #n!##=n*(n-1)!# #...1!# until you get to #1!#

Or simply; #n!##=1*2*3*...n#

#:.5!4!##=(5*4*3*2*1)*(4*3*2*1)#

#rArr120*24=2880#