A., Transports Metropolitans de Barcelona, S. A., y Projectes i Serveis de Mobilitat, S. A., Ferrocarril Metropolità de Barcelona, S. Rights in respect of the data provided : you have the right to access, rectify, erase, limit their processing, oppose or request personal data portability, as specified in additional information.30 of Law 19/2014, in the absence of the information and it being necessary to refer to the body or entity that has the information, your data may be transferred to said body or entity, the applicant having been previously informed, as regulated in the implementing regulation. Recipients of the data : in the case described in Art.Legitimisation of data processing : implementation of the contract and your consent.Purpose of data processing : we process your personal data to give you access to the services and features offered by JoTMBé and to carry out commercial prospecting. Data processing controller : Transports de Barcelona, S.Step 3. Select 3 paintings from the rest 12 to gallery C. There are 12C3 = 12!/(3!9!) ways. Step 2. Select 4 paintings from the rest 16 to gallery B. There are 16C4 = 16!/(4!12!) ways. Step 1. Select 4 paintings from 20 to gallery A. There are 20C4 = 20!/(4!16!) ways. 4 paintings will be sent to gallery A, 4 to gallery B, and 3 to gallery C. We do not need more steps because the 3 digits “1” should be assigned to the 3 rest places by the only way.ģ) An artist has created 20 original paintings, and she will exhibit some of them in 3 galleries. 4 places are already selected for the letters, so there are 4 other places. Step 3. Select to where put the digit “0”. Step 2. Arrange the 4 letters in the assigned places. Because the letters must be put together, they can be put on the 1 st – 4 th places, 2 nd – 5 th places, …, 5 th – 8 th places. Step 1. Select places to where we can put the letters. We do not need more steps because the rest 3 players should be assigned in car C by the only way. Step 3. From the rest 6 players select 3 people in car B. Step 2. From the selected 8 players select 2 people in car A. We count how many ways there are on each step, and then multiply these numbers. To solve these problems, use the Fundamental Principle of Counting: Every arrangement can be done as series of steps. Thanks for your genuine assistance in advance and have a nice day.Ī studious student willing to progress :) Could you please elaborate? Also, why should the sum of the denominator be the same as numerator? In how many ways can this be done?įor this question, I do not know why you include 9! in the denominator to solve this problem. Here is the question: An artist has created 20 original paintings, and she will exhibit some of them in 3 galleries. If both methods are wrong, feel free to tell where are my errors and what are correct methods.ģ) Lastly, there is a question that I saw in class but I did not understand the method for solving this problem. Hence I think that: 4P4 x (4! / (3! 1!) is the method for this question. In this case, we are putting each letter and number together, therefore I think that no repetition is allowed. In this case, we are choosing people randomly, therefore do we need to use combination and divide 10C8 by (2! 3! 3!), to avoid repetition?Ģ) In how many ways can the letters and numbers of MATH1011 be arranged, if all the letters must be put together? I solved 2 questions and I wonder whether my answers are correct.ġ) A coach must choose 8 players randomly from 10 players and assign them to three different cars to transport them to an out-of-town game: 2 in car A, 3 in car B, and 3 in car C.
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