I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

If you're a Gen-X parent, you're in the right place!

# Category Archives: Finite Math

### Freaky Factorials and some Fun Facts that Follow

This is Day 27 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.

Writers have borrowed from the Germans the abbreviation … which gives their pages the appearance of expressing surprise and admiration that 2, 3, 4,etc. should be found in mathematical results.
~Augustus De Morgan

At some point in your math life, you’ll encounter the f-word.

And by that I don’t mean fractions or functions.

I mean factorials.

Like many other math things, these guys aren’t bad to deal with if you remember what they really are. And you aren’t afraid to get your hands a little dirty.

### What is a factorial?

A factorial is a unary operation on a non-negative integer. If the integer is positive, it returns the product of all integers from 1 to that number. If the integer is Zero, it returns 1.

Holy cow… that’s all true, but impossible to understand.

A factorial is an instruction. It says to a positive number: “Multiply yourself with all the other numbers less that you.”

It says to Zero, “Give me a 1. Don’t think about it. Just give me a 1.”

And it doesn’t give any instructions to negatives or fractions/decimals or any other crazy number-like-things. (It pretty much ignores them and refuses to work at all.)

We say something like “six factorial” when we mean .

And since writing out “6 factorial” takes a while, we write 6! instead.

### Six Dammit

My favorite professor would sometimes jokingly refer to the exclamation point as an actual point of exclamation. When we were doing 6!, he would say, “Now we do six dammit.”

And that’s a bit what students might say when dealing with these.

As a math student, you’ll likely encounter factorials in a probability course. Which means you’ll be faced with this expression: .

And you’ll be mighty tempted to reduce the fraction by cancelling out: .

But be careful. Look closely at what these guys mean. And note that factorials fall into “isolation” in the order of operations.

And 120 is not the same as 2!, for sure!

### Freaky Factorial Facts

If you’re careful about that, you should be fine. But factorials are so freaky, that it’s worth noting some of their more interesting facts:

If you have the phone number 362-8800, your phone number is 10!. (I’m dying to call people and tell them this. So far my frontal lobe is doing a great job helping me inhibit these impulses.)

As of right now, the phone number that corresponds to 13! does not exist. Go ahead, call it: 622-702-0800. (Turns out 622 as an area code isn’t used. Yet.)

90! is the largest factorial you can tweet (it has 139 digits). And you can tweet me on that!

200! has 375 digits. This is the same number of characters in the first paragraph of Pride & Prejudice by Jane Austen. The preamble to the U.S. Constitution is much shorter – it has only 327 characters!

### Use Factorials Carefully

Now that you know more about them, you might check yourself before writing something like: “My daughter is turning 4!”

Don’t make her grow up too soon!

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### Standard z-Scores – How to Explain Them

Do you teach standard z-scores? Is it a struggle explaining what they really are? Try this! Continue Reading

### Linear Programming Problems – How to Set Them Up

Do your students struggle with setting up linear programming problems? Do you? Here’s a handy list of steps that will help. Continue Reading

### Probability Tree Diagrams as Puzzles!

Probability tree diagrams are a tool to help students find probabilities. But they can also be a puzzle. Learn how and get the FREE DOWNLOAD here! Continue Reading

### 2 Responses to Probability Tree Diagrams as Puzzles!

1. Alice Petillo says:

Is there a reason why the second example hasn’t been corrected/updated?

• Bon says:

Yes, Alice, there are a few.

1. I’m crazy busy with lots of other things.
2. This is a minor error that only one person in 2.5 years has noticed.
3. The important content of the piece is error-free.
4. I have a list of things to do on the blog that has about 130 things on it.
5. It’s nice to let others discover the error too.

All things taken together, it’s just not even on the list to get fixed.

However, I appreciate you commenting about it so that others will know that when they find the error, they aren’t crazy.

### 2 Responses to Permutations in Braiding Hair

1. Oh, I’m laughing, because this me!

Now, what are the permutations for a fish tail braid? 😉

• Bon says:

Error 509 Bandwidth Limit Exceeded: processing overload in the author’s brain.

### The Math Behind the Monty Hall Problem

As promised, here’s the “hard way” to understand the Monty Hall Problem. A little math involved, but also the Back to the Future Time Machine! Continue Reading

### One Response to The Math Behind the Monty Hall Problem

1. Jim Briggs says:

This is the first explanation I have heard or read that enabled me to understand why you should switch. Great job! It still seems counterintuitive, but at least now I get it.

### The Monty Hall Problem Explained – The Easy Way

There are a couple of ways to explain the Monty Hall Problem – the easy way and the hard way. I have to make cheesy potatoes, so the hard way comes tomorrow… Continue Reading

### 2 Responses to The Monty Hall Problem Explained – The Easy Way

1. Dave says:

I don’t understand. You only have to pick from two doors that you don’t know what’s behind, so the chance is 50/50.

• Bon says:

That’s the point, Dave. It’s kinda not that simple. Creepy and weird, though, for sure!

Thanks for stopping by.

### Present Value vs Future Value – How Can You Tell the Difference?

Ever wonder what the difference is between a Present Value annuity and a Future Value annuity? Wonder no more! This video explains it. Continue Reading

### 7 Responses to Present Value vs Future Value – How Can You Tell the Difference?

1. Gabrielle says:

This helped me so much! Its so simple now oh my god

• Bon says:

2. Deb says:

This was so helpful! Thank you!

• Bon says:

3. Elisa says:

Omg, thank you so so much. I really needed help and this was such a great help! Thank you!

• Bon says:

Awesome, Elisa! Thanks for letting me know!

### Math Crafts: Probability Earrings

Want to get your homeschool teenager to do probability? Try heading to the bead shop first. This video shows probability in action with a beautiful end result. Continue Reading

### In How Many Ways Can You Solve the Thiagi Circles Jolt?

A fun puzzle from world famous Thiagi – and the number of different ways to solve it! Continue Reading

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Calming generation X in math since 1985.

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