The Fundamental Counting Principle

This precalculus video tutorial provides a basic introduction into the fundamental counting principle. Examples include the problem with how many different outfits one can wear, the multiple choice test, and telephone numbers.
Permutations and Combinations:
• Permutations and Combi...

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[@mallomia]

My Algebra teacher sucks at actually explaining, so you have been a godsend, Mr. Organic Chemistry

[@Aneeqaslayss]

Just a note, for the tree diagram you can also count the last row for the number of possibilities instead of counting each and every possibility.

[@friedavi]

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[@samueljamieson6677]

Probability that Mike's outfit looks goofy: 100%

[@kgolanekgotlelelomarota7682]

Don't you mean 1.? 🫡

[@calebchastain]

Thank you so much for simplifying this!

[@dqggers_]

what happens if i call those phone numbers

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[@4funsies499]

"Weird outfit, but for the sake of this problem..." lol math questions are so questionable sometimes

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[@gwenalimpolos5419]

do you have pigeonhole principle

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[@heathermoore9008]

Can this work with solving a rubix cube?

[@RajitChy22]

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[@blackhand441]

Wait about that second example sir
If the first digit of the seven digit code isn't going to move from that position wouldn't it be like
(8*10²) + (8*10⁸)

[@AliceKMay]

I don't really get your question but hope this explanation will help you.
The fundamental counting principle states if there is n way to do smth and m ways to do another things, the total possible outcomes would be m*n.
So there is a limitation in the first 3 digits and local number (not 0 or 1), you can only choose from 2 to 9, which is only 8 outcomes. For the rest, you can choose from 10.
And if you want to find total possibilities, multiply everything.

[@abdulhamidsiad7846]

@@AliceKMay just a quick question since we already used the number 8, wouldn't it become 7 for the beginning of the 7-digit number after the 3 area code. because 7 isn't 1 or 0 is there any reason why. I hope this is making sense and that reply was awesome great explanation there.

[@AliceKMay]

@@abdulhamidsiad7846 I think you're confused with digits and possibilities. In this problem, we are thinking how many digits are possible to be added in a telephone number.
8 means 8 possible outcomes (2, 3, 4, 5, 6, 7, 8, 9). Not the digit 8.
Hope this helps!

[@Lazer8Heart]

@@AliceKMay thanks, cleared my doubt

[@StacyMintzy]

I cant understand number 2

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[@vitaly768]

For the thrid problem the answer is 100.
Since this is a multiple choice quiz, we have 25 ways to answer a question
(let's say our options are A, B, C, D and E):
A B C D E
AB BA CA DA EA
ABC BAC CAB DAB EAB
ABCD BACD CABD DABC EABC
ABCDE BACDE CABDE DABCE EABCD
Then, we multiply number of options to anwser one question by 4 because we have 4 questions: 25*4=100

[@axoltlbunny8955]

Not exactly. Because of the context of the problem, you solve it differently than the first problem. In #1, you don't repeat any letters because it wouldn't make sense to wear 2 pairs of pants at the same time. However, in a multiple choice test you could pick A for all four problems.

[@laudergy]

There's actually 31 ways to answer a question since 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 31. If you include no answers, then it's 32. In a multiple choice question, you don't use permutation (nPr), because you don't need to answer them in order. ABCDE, BACDE, CABDE, DABCE and EABCD are the same. Instead, use combination (nCr).
Anyway, neither permutation nor combination works here. Idk why tho. My brain just can't anymore.

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1000th like, cool

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first person to comment

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