Evaluate two factorial over seven factorial.
The exclamation mark here represents factorial and a factorial. We will begin here with the number 𝑛 and multiply that by 𝑛 minus one and multiply that by 𝑛 minus two, all the way down until you’re multiplying 𝑛 by one.
In the case of two factorial, it’s just two values, two times one. But seven factorial is seven times six times five times four times three times two times one.
One way that we can think about simplifying factorials is rewriting them. If we leave two in two factorial, we can break seven factorial up into seven times six times five times four times three times two factorial. In this case, you have a two factorial in the numerator and the denominator. And they cancel out.
This is also true if you write it out. Two times one in the numerator, two times one in the denominator cancel out. And we’re left with one over seven times six times five times four times three. When you multiply all of those values together, you get 2520.
We evaluated our expression and found one over 2520.