Hey everyone. Andrew here. Today we went over yesterday's worksheet on the Fundamental Counting Principle. We also had our first quiz! Yay! After both of those things, we continued with our lesson on Factorial Notation.
Firstly, we learned how to simplify. To do this, you can expand either the numerator or denominator.
For example, say you have a question like this: 5!/4!
You can expand both of them so that you'd get something like this: (5x4x3x2x1)/(4x3x2x1)
Then, you just cancel out like terms so that you end up with just 5.
Another way to do this would be by expanding only one of the two (Numerator or Denominator) so that you end up with a different, lower factorial.
For example: 12!/8!
You can just expand the Numerator: (12x11x10x9x8!)/8!
Then, just cancel out the 8!, so that you are left with: (12x11x10x9)
Finally, just multiply them all together to get 11880.
The final thing we learned today is how to solve for n.
Firstly, isolate n.
Then, cancel out what you can. If you can't, expand something until you can.
Eventually, you should get something that looks like this: ax^2 + bx + c = 0
Then, you can just solve the square. You will get 2 x values.
Finally, plug in the two x values one at a time to check.
*Remember: the x value CANNOT be negative!
That's about all. See ya all later!
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