Introductory Statistics Unit 1 Session 1

追加: 2026-05-17

[00:00:01][Music] welcome to this course introductory statistics one my name is Salas baji I'll be taking you to this course basically this course is about the basic concept of probability we have six unit to do with without Much Ado I would like to begin with the first unit unit one which has six sections so unit one combinational analysis with section one fundamental principles of counting by the end of this session we should be able to State the fundamental principles of counting and explain those principles give at least two examples and also how we can apply those principles of counting analyze problems and identify tax in them let's get deeper suppose I have X number of Tres and Y number of shes to dress up weights well those X number of shed and Y number X number of trouses and Y number of shed are going to give me a different Outlook or different appearances so how many appearances will I have if I to use those X number of Tres and Y number of shs well real this task can only be accomplished by me wearing the X number of trousers followed by the y number of shirs and in this case I'm going to have y * n or x * y sorry different ways of dress up you get it so you're going to have X by y different ways of appearance so to say so you realize that but this type of counting by combining one I element with another one is what we refer to as fundamental principles of counting and this principle can be used for counting in probability Theory maybe we would like to take a concrete example to see as example one suppose I have two pair of Tres and three shirs assuming that each pair of Tres can be worn with each shirts how many Tres shirt outfit do I have now to make this more easily for us to understand let's identify those two trouses as being the color of black and brown and let's identify the colors of those shirts possibly white blue and yellow so if I pick the black trouser I could wear the white or the yellow or the blue shirt on them giving me three different appearances and when I pick the brown trouser I could also wear the white the blue and the yellow shirt on it equally give me also a different three different appearances in all I'm having six different appearances and how do we arrive at this six that is we multiplying multiplying the the number of trouses I have by the number of shed as you can see that is 2 * 3 that will give us the six different trer outfit that I can choose from let's move on with more example example two how many number of three different digits can be formed by choosing from the digits 3 4 5 6 7 and 8 now how can we carry out this task now we are forming three digigit number so what it means is that we can break this problem into three tax what are the taxes we are talking about by selecting the 100th digits the 10 digits and the ones now I have six numbers so if I were to choose a 100 digits I have six choices to make six numbers to select from so I have six different ways or six different choices that's selecting the hundreds now assuming that I have we done with that selection now the next to choose from is a 10 digits so one number is gone as we select the 100 so how many numbers will be left for us to select the 10 that would be only five numbers to the 10th digit from and we move on to the one digit we left with what four numbers to choose from so in total we're going to have 6 * 5 * 4 which equal 120 different 3dit numbers to form hope you got the point clear yes maybe let's move on to another example to get the concept clearer how many numbers of three different digits can be formed by choosing from the digits 3 4 5 6 7 and 8 but listen to the last part of the question if the numbers can be repeated unlike the previous example that example two the numbers could not be repeated so once one number is speak it reduces the total number of numbers we have there but if this we also have three TX to car on this despite the repetition so we need to select from the 100 digits or you select the 100 digit the 10th digit and then the one dig yes so how many choices do we have to select the from this numbers what will I have I have six choices to make to select the 100 digits because the number could be repeated what it means is that I can say choose the same number again so selecting the 10 digit I still have six numbers to choose from that have six ways because repetition is allowed and selecting the one digit also I still have six numbers to choose from yes in conclusion what will be our final solution so we going to have six * 6 * 6 = 216 different 3digit number to select so you see these are some examples of principles of counting yes we're able to learn this fundamental principles of counting as a review and we have seen examples of those principles and we able to analyze the problem involving those principle thank [Music] you