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Geometry Lesson 12-8 "Counting Methods & Permutations"

Added May 02, 2017 •

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four five six seven eight nine in the algebra book so you can find the possible orders of objects by making an organized list a tree diagram don't even remember making tree diagrams back when he gets everybody see if you have got them all the possibilities sorry first example we're going to be making a tree diagram you guys are only have to make one of these on the assignment today they might review it but I'm going to do samples on right now the nightmare Falls Road can I see a picture of three shirts and two pair of pants that coordinate well make a tree diagram to find the number postal outfits you have so please say it since you paragraph This will be a tree diagram so you can make sure crime report one or two shirts with pant one or two or three with camo pants suit see you have one two three four five six possible outfits to be made out of those 3 shirts and 2 pairs pants so you guys are going to make one now for checking if any more suppose you have two shirts and four pair of shorts you can bring food make a tree diagram to find number of possible outfits for gym so t-shirts and four pair of shorts  make a tree diagram to model the outcomes show me a short poem or short to and with each swords making 1 and 1/2 trade bobcat for I can get my shorts but that's okay I didn't I didn't mean to ask this anyway loops venomous Churchill you can go to Camp wine can't to Camp 3 or pant for so you have 8 Prince outfits possible with those combinations questions on the tree diagram oh I forgot to ask you one more question would you like to use a tree diagram to find the number of search for five t-shirts and eight pairs of shorts k 40 Oak dress and how did you get that so quickly say that Health First it says we call them and one of them does not affect the result of the second event the events are independent events are independent you can find the number of outcomes using the multiplication counting principle so as you guys just realize MD  example Vine that you can find how many outcomes are by multiplying the number of church by the Numbers pants and that'll tell you how many total combinations there are today's events are independent of each other call the multiplication counting principle if there are M ways to make a first selection and end ways to what is second selection there RM times and ways Road but to make the two selections that's called the most location counting principle so let the fire starts at 8 for me to take 5 x 8 and get 40 different possible outfits sad example 2 says on the map there are two tunnels for cars getting from New Jersey to Manhattan New York Manhattan New York and Bridges from Manhattan to Brooklyn New York how many routes using a tunnel and then a bridge are there from New Jersey to Brooklyn true Manhattan so there's three Bridges and two tunnels surgery * 2 is  sex Fado 6 routes which I'm assuming this is check on her sitting chair at the neighborhood pizza shop there are five vegetable toppings and meat toppings for pizza how many different pizzas can you order with one meat and one vegetable topping so using the counting principle will take 5 x 3 to give 15 different pizzas screen filter that is example 1 please  why would you do 5 times 5 it doesn't matter what order cuz you have five toppings you can pick one of those five toppings  and that old veggies and then play me toppings and get one of each so 5 x 315 okay find the number for arrangement of objects and said this is not an example this is leading into the next example one kind of candy Miss to find the number of possible Arrangements of the objects in a set here are the pot arrangements for the letters a b and c without repeating any letters a b c d a c c a b a c b c a n c how many different outcomes there 6 outcomes MK6 outcomes each of these Arrangements is called a permutation commutation is an arrangement of objects in a specific order example today how many different batting orders can you have with 9 baseball players so  if you have 9 players and want to put them in a lineup. How many players are have to pay it for the spider does mine player the first batter now how many arrive to pay for the second batter and then the third daughter and then the fourth bottle okay so back to the biggest turtle combinations find players everybody know an easy way to find an answer  9 factorial so you should have has an exclamation point on your calculator  do I help Minecraft sex or you might have to go and hit a prb but some people kprb that's for probability say depends on your calculator cuz you guys do this for mrs. check on the same three as swimming pool has eight Mayans and how many days can a swimmers be assigned plans for a race okay so if you could run swimmer for the first line out of Spanos home at 7 for the next one in six five four three two one and so on your calculator 8 factorial 40320 cartoons on that in how many ways can you survive a right center and left fielder players on a baseball team to answer this question you need to find the number of permutations of 8 objects squares arranged three at a time  person to find how many ways you can select a right center and okay. 3 positions from eight players  find the number of permutations of 8 objects are players and situation arranged three at a time so permutation notation we're going to do this problem in just a second NPR Swiss is a little and a capital P in a little are represent the number of permutations of n Jax events are at a time so we're going to have 8 players almost liking three positions so 8pr would be our the MP3 will be having to set that up 8 players season 3 of the time for the three Outfield positions famous taking 8 x 7 x 6 wheels to choose for the left-field so that leaves seven for Center N64 white zebra take 8 * 7 * 6  Sebastian and 36 ways you also on your calculator that looks like this  so depending on your calculator I put eight and then stats what does mm3 and I guess leave the same result so check your calculator and see if you have that button if you have bacterial you should have say maybe in the PBR if you have that PBR team the probability or prv example for 7mm NPR horror persevere what that means is taste 7 times 6 times 1 times 4  but you can also use that key can you get 840  so you still want to understand what's going on when you hit that key so you may want to write if it's not too much right now just so you remember what's actually happening when you hit back heat okay saved by CBS 3 check understanding for what you get for a 504 210 27 x 9 x 8 x 7 when you read this one out is 7 * 6 * 5 play some good five times for if you let him out in simulcast nothing in some situations order Matters by repetition is allowed this is when they were abused something possible repetition is not allowed that's when you would use permutations to talk about the counting principle and location today  postal room that consistently survive when is the counting principle when repetition is not allowed how many patients make a note about that  Thomas is actually example 5 coming up not 6 top five examples so this is the last one supposed to use six different letters to make a computer password find the number of possible 6 letter s words 6 different letters so  repetition is not allowed citizen penetration 76 different letters how many letters do we have to choose from so 26 with a choose the latter there's 25 24 23 22 that would be the same as taking sick 26p 6 on a calculator 26 chosen 6 Elsa Frozen alphabet to pick from Total dad and 65765006 Ed Davis replace at six different letters tomorrow tomorrow combinations for when we will pick basking involved and repeating the water so she ain't love everything's going to be different hey check this game 5 last one suppose your cousin needs to choose a four digit number to use with a new debit card the number of possible 4 digit numbers without repeating a digits  0 is a digit as well  four digit number you're not allowed to a picture cellular 10 digits for the first number 0 to 9 and then 9 a 7 or you can do 10 P4 can you get 5040 kmm Part B says is a six-letter password or a 6 digit number order for explain the password video harder to guess because a lot more because of this * 26 letters we don't start with 10 digits and there's a lot more outcomes okay so tomorrow we will talk about combinations  call me back

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Geometry Lesson 12-8 "Counting Methods & Permutations"

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