Counting Principle, Permutations, and Combinations

I work through the Fundamental Counting Principle at the beginning of the lesson. At 6:03 I use the idea of playing the lottery to develop the idea of Permutations and Combinations. At 15:00 I give the formulas for Permutations nPr and Combinations nCr and work through two last examples.

Professor,

I have no quibble with your method of instruction. You were quite clear and very thorough; however, there was an issue of terminology that bothered me. You kept using the phrase 'odds of winning,' when what you calculated was actually the probability of winning. Odds and probability are not the same thing.

Granted, when the probability of winning is very low, as in this case, the odds of winning and the probability of winning have approximately the same value but they are nonetheless not the same concept. Odds is a ratio that bookmakers use to handicap horse races, and it is usually stated in terms of 'odds against winning' rather than 'odds of winning.' Odds...against... are the number of times that you should expect to lose vs. the number of times you expect to win. Odds...of winning... then is the inverse of odds...against.

If an event has a probability p that you'll win, it also has a probability 1 - p that you'll lose. The odds...against winning... are
(1-p)/p. Simplifying this expression, Odds = 1/(p - 1). When 1/p is greater than 1, the trailing constant may be safely neglected, and the Odds ...against winning... become approximately 1/p. Flipping this ratio upside-down, the odds... of winning... are likewise approximately equal p. Probability and odds may be approximately equal but they are not the same thing.

[david]

This is the kind of energy that I want so I can actually learn, my past teachers are so emotionless when teaching math so I'm always bored. Anyways you have very beautiful hand writing


Watching from Philippines btw☺️
Madaming salamat po
*Thank you very much

[shapi]

I was saved by your teaching before and I literally got a perfect grade in my math final exam and ever since then, I would always come back to your channel if I ever got myself in trouble with maths!

[emilywo]

Hi Mr. Tarrou, just wanted to say thanks in general for all the help you've given to me this year! Because of your videos I was able to do well in precalculus and improve in math. You're a great teacher!!

[mom]

Thank you so much for your excellent video. I homeschool our children and 7th grade math has somehow escaped my memory. Today after watching your video not only did we understand the permutations and combinations, but it was fun to learn. Wish I would have had a teacher like you when I was in school. Keep up the wonderful work!

[hannahwolf]

Dear Mr Tarrou,
I absolutely love mathematics. Seeing these videos and your mutual love for the subject makes me so happy. You inspire me to continue my dream of teaching and sharing my love of problem-solving with everyone else in a fun and interesting way. Thank you for all that you do. :-)
Best regards, Hannah Wolf

[AsianNationGaming]

These are actually really cool and engaging, might I add done in very clean and easy to read handwriting. Many props, I really want to see this grow to be something big! I found myself watching videos of yours on topics I wasn't really studying for but picked up rather easily.

[profrobbob]

My new #math  lesson is now Closed Captioned

[georgesadler]

Professor RobBob, thank you for a tremendous video/lecture on Counting Principle, Permutations, and Combinations. This material is the beginning of Probability and Statistics, which is a different way of thinking in mathematical terms. Probability and Statistics is another mathematical world that students can encounter in the near future, if they are interested.

[brucemcconkie]

Wonderful, very well thought out and prepared, his energy is awesome, perfect.

[fahimma]

Hello! Mr.Tarrau you are a real inspiration for me.I am going to sit for GCSE Exam and your videos are really helpful.Thank you very much.I really encourage you to continue further with such helps.

[parnikakapur]

Thank you so much for this lesson. I understand the difference between permutations and combinations much better than before. I have a test tomorrow, and I am relying on your videos in addition to my notes.

[AnnaDocmen]

Oh my god. You saved me! Thanks for explaining this so nicely

[ScienceGeek]

You have beautiful handwriting, all my students agree

[atifbashir]

Impressed by the way you teach and your writing is awesome

[rishitshah]

you are really great sir..
how easily you cleared our doubt and the concept
(but really must have took much time to make this video )
Thank you sir

[teddyw.charawa]

Your handwriting drives me nuts. It is so great!!!

[kyasunderland]

Again, thanks endlessly for saving me when it comes to maths

[sayamina]

Thank you so much! So ready for that quiz tomorrow!

[Frankx]

U deserve more subscribes, Clear, Easy, Enjoyable

[marjorielouis]

Wow! Thanks for explaining the steps and the reasoning to the formula. I have a better understanding of solving the problems.