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## Pixar in a Box

### Unit 13: Lesson 2

Counting crowds- Start here!
- 1. Two headed robots
- Counting two-headed robots
- 2. Snake bots
- Building snake bots
- 3. Calculating factorials
- Calculating factorials
- 4. Casting problem
- Counting casts 1
- 5. Does order matter?
- Counting casts 2
- 6. Binomial coefficient
- Combinations

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# 3. Calculating factorials

Now that we have a feeling for constructing permutations let's introduce the factorial formula to make counting them easy.

## Want to join the conversation?

- Do you actually use 10! in Pixar to create robots and if so, how do you narrow your choices down?

Loving these lessons!(6 votes)- Probably they either chose their favorites or didn't use that many parts...(5 votes)

- I don’t understand this is too hard(3 votes)
- Well since every piece is used oned per snake bot(1 vote)

- Are there any properties of factorials that would be useful to know, such as dividing them or multiplying them? Thank you!(2 votes)
- Well say you have 24!, but you only wanted the first few.

Then you can say you want 24x23x22x21. So just do 24! and divide it by 20 factorial and there's your answer (:

You can check more on Numberphile, if you like, I find their videos really helpful ^^(2 votes)

- I though i was going to have to do the 10 colours for a second(2 votes)
- I think it is called Permutations in calculus.(1 vote)
- Hi!

Here from sigma notation, I'm just curious, sigma notation lets you specify what number you'd like to stop adding. Can factorials do this?

Thanks!(1 vote) - This snake is over 9,000! But seriously, does Pixar ever use that much?(1 vote)
- Oh? What the heck is that? 3 628 800?(1 vote)
- I dunno this hard math im only n class 4!(1 vote)
- Does anyone know the history behind using an exclamation mark above and slightly in front of a number as the factorial sign?(1 vote)

## Video transcript

- Nice work! Suppose we wanted four-segment Snake Bots as in the previous exercise. How many of those are there? Well, we have four choices
for the first segment, three choices for the second segment, two choices for the third segment, and one choice for the fourth segment. So that's four times
three times two times one, which multiplies out to 24. Isn't it interesting that
you can make 24 different Snake Bots using only
four different objects? And it gets better! Suppose you wanted a
ten-segment Snake Bot. Then you could make ten times nine times eight times seven times
six times five times four times three times two times
one different combination! Which amounts to a whopping 3,628,800 different ten-segment Bots! And you only have to build
ten different objects! These kinds of calculations
appear all the time in combinatorics, so of
course mathematicians invented a name and a shorthand for them. They're called factorials, and they're represented with an exclamation point. For instance, four exclamation point, or four factorial, stands for four times three times two times one. So four factorial is 24, five factorial is 120, and 10 factorial is over three million! Wow! That's a combinatorial
explosion of choices! (glass-shattering blast) Let's pause now and practice this concept in the next exercise.