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nice work suppose we wanted four segments 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 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 different combination which amounts to a whopping three million six hundred twenty-eight thousand and eight hundred different ten segments 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 let's pause now and practice this concept in the next exercise