99% Of People Fail This Factorial Problem! | Can You Solve It?

Added: 2026-06-02

[00:00:00]All right, lads. It's Danny here today to bring you a lovely video. In today's video, we're going to take a look at something very, very interesting. A very interesting problem, you know, it looks very tricky at first, but it's actually a very, very nice-looking problem because it's it gives you a nice answer at the end, and it could be easily calculated without a calculator. So, that's very interesting. I'll show you how to solve this. The goal of this question is to solve for the missing end term. So, I'll show you how to do that.

[00:00:31]But before we jump into it, I want you to leave a like and subscribe. So, this question here is pretty famous, and I'll show you how to solve it without using a calculator, and it's very, very interesting the the way and the method we use to solve it. So, the first thing that you're going to need to understand is what a factorial is, and the most basic term of a factorial is, let's say you have 3!, you can rewrite it as 3 * 2 * 1, and that's going to be equal to 6.

[00:00:59]And we could do that, you know, so on and so forth. But in this problem, we have 6! and we have 3!. So, 6 would be the same concept. Instead, you're going to be going all the way from 6 to 1 being multiplied. So, anything in between, but basically, right? 6 * 5 * 4 * 3 * 2 * 1 is going to be equal to 720.

[00:01:19]This information is very useful because we can substitute this in into our equation over here. So, let's do that straight away. 6!, what is 6!? Well, 6!

[00:01:30]is 720. So, in the numerator, we're just going to have 720.

[00:01:35]And, you know, what's 3!? Well, 3! isn't it just 6? So, we're left with in the denominator 6!.

[00:01:44]And looking at what 6! is, we already solved it over here, which is equal to 720. So, we're going to basically put it as 720.

[00:01:53]In the numerator, however, this is where the trick basically comes in.

[00:01:57]We are going to take 720, remove it from the factorial basically. So we're going to have 720 * 719!

[00:02:06]So when we do this, we can factor out the 720.

[00:02:10]So let's do it cuz it shows up in the numerator and shows up in the denominator. And when you do that, what you just are left with is 719! = n! The factorial, you know, are going to cancel out really because you have a a factorial on the left-hand side and right-hand side you're trying to find what term will give you 719!

[00:02:31]And that's just going to be 719, so that's how you solve this interesting looking problem. So if you all enjoyed this video, please drop a like and subscribe and I'll see you all later.