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tanszek:oktatas:techcomm:combinatorics_exercises

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tanszek:oktatas:techcomm:combinatorics_exercises [2024/10/08 12:28] – kissatanszek:oktatas:techcomm:combinatorics_exercises [2024/10/29 10:29] (current) – kissa
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   - A shipment contains 100 boxes: 75 are quality $A$ and 25 are quality $B$. How many ways can we select a 12-box sample in which the quality $B$ goods do not exceed 30%? //(686,128,883,942,025)// \\ \\   - A shipment contains 100 boxes: 75 are quality $A$ and 25 are quality $B$. How many ways can we select a 12-box sample in which the quality $B$ goods do not exceed 30%? //(686,128,883,942,025)// \\ \\
   - 12 students rent three boats: one with 3 seats, another with 4 seats, and the third with 5 seats. In how many ways can they be seated in the boats? //(27,720)// \\ \\   - 12 students rent three boats: one with 3 seats, another with 4 seats, and the third with 5 seats. In how many ways can they be seated in the boats? //(27,720)// \\ \\
-  - How many five-digit numbers starting with 15 can be formed using the digits 1, 3, 5, 7, 9, if each digit can be used only once? //(6)// \\ \\ +  - How many five-digit numbers starting with 15 can be formed using the digits $1, 3, 5, 7, 9$, if each digit can be used only once? //(6)// \\ \\ 
-  - In how many ways can the letters of the word MATHEMATICS be arranged (i.e., permutations of the word)? //(4,989,600)// \\ \\ +  - In how many ways can the letters of the word $MATHEMATICS$ be arranged (i.e., permutations of the word)? //(4,989,600)// \\ \\ 
-  - How many four-digit even numbers can be formed using the digits 0, 1, 2 (with repetition allowed)? //(36)//\\ \\+  - How many four-digit even numbers can be formed using the digits $0, 1, 2$ (with repetition allowed)? //(36)//\\ \\
   - 10 students qualified for the university sports day running competition. The first 3 will receive medals. How many different ways can the list of medalists be arranged? //(720)// \\ \\   - 10 students qualified for the university sports day running competition. The first 3 will receive medals. How many different ways can the list of medalists be arranged? //(720)// \\ \\
   - We roll a standard die four times in a row, and we write down the results of the rolls in order. How many different four-digit numbers can we obtain this way? //(1,296)// \\ \\   - We roll a standard die four times in a row, and we write down the results of the rolls in order. How many different four-digit numbers can we obtain this way? //(1,296)// \\ \\
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     - each flag must have two stripes? //(12)//     - each flag must have two stripes? //(12)//
     - each flag must have three stripes? //(36)// \\ \\     - each flag must have three stripes? //(36)// \\ \\
-  - After a graduation ceremony, each student in a student circle received a photo from each of their classmates. How many students graduated if a total of 992 photos were exchanged? //(32)// \\ \\ +  - We placed a $red$, a $white$, and a $black$ dice in a box. We randomly draw two and roll them. How many possible outcomes are there for this experiment? //(108)// \\ \\ 
-  - We placed a $red$, a $white$, and a $black$ dice in a box. We randomly draw two and roll them. How many possible outcomes are there for this experiment? \\ \\+  - After a graduation ceremony, each student received a photo from each of their classmates. How many students graduated if a total of 992 photos were exchanged? //(32)// \\ \\ 
tanszek/oktatas/techcomm/combinatorics_exercises.1728390534.txt.gz · Last modified: 2024/10/08 12:28 by kissa