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# Probability with permutations & combinations example: taste testing

We can use combinations (when order does not matter) and permutations (when order does matter) to find probabilities. Created by Sal Khan.

## Want to join the conversation?

• who like to drink olive oil?
• why is it a one on top if they pick three different types?
• Shouldn't it be 1/15C3 * 1/15C3? Because not only are you calculating the probability that the participant guesses some 3 specific flavors; but also that those are the 3 selected by Samara.
• I thought that permutations meant that ABC is not equal to BAC, meaning that we don't care about the order, so they both add to the list of permutations individually. But am I interpreting the way we use the word "care" in this case wrongly?
But there would be more outcomes if we didn't care about the order, as instead of just having any one-order-of-letters, ABC, for example, replacing ACB, BAC, BCA, CAB, and CBA, meaning that we would always have more outcomes when using permutations.
In this case, we wouldn't be trying to guess in the right order the three different olive oils, so long as we choose the right three types. Wouldn't that mean that we need to deal with permutations to solve this problem?
But then, at , Sal stated that trying to use permutations would mean that we'd have to guess the correct order. But permutations means that ABC, CAB and BCA, etc. are are different, indicidual permutations, right? Meaning that we wouldn't be needing to guess the correct order, which the question states we don't need to do, guess the correct order of olive oils mixed together.
• This is my second time through this lesson (first in statistics, now precalculus) and I still can't quite explain to myself why we do - let's say the combination of 5 items in 3 slots = so 5 C 3, which means that it's 5x4x3 divided by 3x2x1. I mean I understand it enough to solve, but I'm not satisfied, missing some extra spark of insight.
(1 vote)
• So you seem to understand the content. You found nPr which is 5*4*3. You then took into account the number of positions. You did this by dividing by 3*2*1 or in other words 3!.

To put it another way nCr = n!/[(n-r)!*r!], where n is the number of object. r is the number of positions available.

The key idea to derive this formula is the rule of product axiom (refer to Wikipedia if need be). An axiom is a statement that is true and cannot be proven.