Question

Evaluate the following expressions.
a. 9!/8!
b. 7!/5!
c. 21!/19!
d. 8!/4!

Answer 1

Answer:

Remember, $n!=1*2*3*\cdots*n$, then

a)

$\frac{9!}{8!}=\frac{1*2*3*4*5*6*7*8*9}{1*2*3*4*5*6*7*8}=9$

b)

$\frac{7!}{5!}=\frac{1*2*3*4*5*6*7}{1*2*3*4*5}=6*7=42$

c)

$\frac{21!}{19!}=\frac{1*2*\cdots*19*20*21}{1*2*\cdots*19}=20*21=420$

d)

$\frac{8!}{4!}=\frac{1*2*3*4*5*6*7*8}{1*2*3*4}=5*6*7*8=1680$