How do you simplify (7!)/(3!)?

2 Answers
Apr 26, 2018

The result is 840.

Explanation:

You could use a calculator and actually expand it all out, or you could use the recursive definition of the factorial:

x! =x*(x-1)!

For instance, 8! =8*7!. In our problem, you will see that eventually, things cancel out.

color(white)=(7!)/(3!)

=(7*6!)/(3!)

=(7*6*5!)/(3!)

qquadqquadqquadvdots

=(7*6*5*4*3!)/(3!)

=(7*6*5*4*color(red)cancelcolor(black)(3!))/color(red)cancelcolor(black)(3!)

=7*6*5*4

=42*5*4

=210*4

=840

You can use a calculator to check your answer:

https://www.desmos.com/calculatorhttps://www.desmos.com/calculator

Hope this helped!

Jul 8, 2018

840

Explanation:

Recall that 7! =7*6*5*4*3*2*1 and

3! =3*2*1

This allows us to rewrite (7!)/(3!) as

(7*6*5*4*3*2*1)/(3*2*1)

We cancel out common factors on the top and bottom to get

(7*6*5*4*cancel(3*2*1))/cancel(3*2*1)

=>7*6*5*4=840

Hope this helps!