The Multiplication Principle

A long time ago (last month) in a land far, far away (from wherever the hell I come from) there was a math module craftily named “Methods of Counting”.

“Wowie”, said the students, “We’re gonna learn how to count!”

“But no” said the evil lecturer, “I’ll have you learn how to count better!” Muaahahahahahahaaa…..

For instance, if you had a certain number of friends, but not enough tickets to a concert, can you count the number of ways you could distribute them?

The way you could think of this problem is by looking at it in terms of choices, in the sense that concerning each ticket, you have a choice of who to give it to.
At every turn in life you’ve got a choice to make from a number of options. In the case above, each “turn” you’re given the choice “who the fuck do I give this ticket to?”

Well, you’ll slowly whittle down your friend group with each turn (not because you lose popularity, rather you don’t wanna give the same fucker two tickets, do ya?), so at each turn you’ve got one less option than the previous.

This is just one case where the multiplication principle comes in handy. Summing up all the possible outcomes, you take the number of possible options at each “turn” and multiply them all together to get that sum total.

This is easily verified graphically by drawing a “choice tree”.

I whipped this beaut up in Paint just now!

There you can see the big idea.

Imagine something simpler, like choosing a combination for a combo lock! You have 4 “turns” each with 10 “options” or “choices”. Can you draw the tree for that one?

No, don’t do it, it’d be a pain in the tuckus. But long story short, there’d be 10^4 possible combinations for a pin code like that.

This concept is used in the definition of the Permutation of a Set, which in turn is used in the definition of the Combination of a set.


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