tanszek:oktatas:techcomm:combinatorics_exercises
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| tanszek:oktatas:techcomm:combinatorics_exercises [2024/10/08 11:50] – kissa | tanszek: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%? // | - 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%? // | ||
| - 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? // | - 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? // | ||
| - | - 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 |
| - | - In how many ways can the letters of the word MATHEMATICS be arranged (i.e., permutations of the word)? // | + | - In how many ways can the letters of the word $MATHEMATICS$ be arranged (i.e., permutations of the word)? // |
| - | - 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 |
| - 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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| - How many subsets of the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ have at least 7 elements? //(176)// \\ \\ | - How many subsets of the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ have at least 7 elements? //(176)// \\ \\ | ||
| - We have fabric in $red$, $white$, $green$, and $blue$ colors, and we want to make flags. Each flag consists of horizontal stripes, and adjacent stripes cannot be the same color. How many different flags can we make if: | - We have fabric in $red$, $white$, $green$, and $blue$ colors, and we want to make flags. Each flag consists of horizontal stripes, and adjacent stripes cannot be the same color. How many different flags can we make if: | ||
| - | - each flag must have two stripes? | + | - each flag must have two stripes? |
| - | - each flag must have three stripes? | + | - each flag must have three stripes? |
| - | - 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? | + | - We placed |
| - | - We placed red, white, and 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.1728388237.txt.gz · Last modified: 2024/10/08 11:50 by kissa