Combinatorics - practice problems - page 4 of 55
Number of problems found: 1090
- Morse code 2
We have two characters, a dot and a comma. How many two-element and how many three-element characters can be created with repetition? - After-school club
30 children in the school club need to split into two teams. They put 15 white and 15 black marbles into a basket and draw lots. The teams will be made up of children who draw marbles of the same colour. Patricia drew first and pulled out a white marble. - In class 24
There are a total of 16 students in the class, a quarter of whom are girls. We randomly select a team of five. Determine the probability that the team will have: a) at least 4 girls. b) at most 1 girl. c) no girls. - Christmas 4
There are only 3 packages left under the tree - two for Julka and one for Zuzka. Julka took two at once. What is the probability that both belong to her? - Members 2
The members of a housing cooperative elected a seven-member board. In how many ways can a chairman, vice-chairman, treasurer, and recorder be chosen from among them? - Books in Slovak and English
Vlasta has 4 Czech and 3 English books. She wants to arrange them on a shelf so that Slovak books are first and then English books are second. How many ways are there to do this? - Beads
We have 4 beads. One is green, one is yellow, and 2 are pink. In how many possible ways can we string them on a string? - Repeatition not allowed
How many four-digit numbers can be formed from the numbers 3 5 8 9 if they are not allowed to be repeated? - The Celebration
Five boys and five girls were nominated for a celebration at a local school. How many ways can the prom king, prom queen, and two other students be chosen from those nominated? (The king must be a boy, and the queen must be a girl) - Playmakers + coach
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game? - Rubber drawing probability
The grandfather bought 10 rubbers for 10 grandchildren. In the bag were 3 blue, 2 green and the rest red. Hansel would like blue gum. What is the probability that Janek will draw a blue rubber if 2 cousins have already drawn it before him and drawn blue a - Die roll probability
If we roll one die, what is the probability of rolling a number other than 1? - Ball selection choices There are 15 black and 15 white balls in an opaque bag. Elenka took one ball out of the bag three times. what choices of the three balls could she choose?
- Aquaristics
We consider “words” (i.e. arbitrary strings of letters) obtained by rearranging the letters of the word “AQUARISTICS”. All letters are distinguishable from each other here. The number of such words that also contain the expression “CAVA” (as consecutive l - Chip number probability In an opaque bag are chips with numbers from 1 to 20. What is the probability that we will draw a chip with a number less than 16?
- Chess club probability
The chess club has 5 members, including two girls. The circle leader wants to determine by lot which member will represent the circle at the representative tournament. What is the probability that a girl will be drawn? - Product defect independence
The product has a 10% probability of an appearance defect, a 6% probability of a functional deficiency, and a 3% probability of both defects simultaneously. Are the random events A - the product has an appearance defect and B - the product has a functiona - White ball probability
We have 10 red and 10 white balls. We will take 5 white. What is the probability of picking a white ball? - Natural numbers
Find the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, 8 occur at most once and not contains any other digits. - Four-digit natural numbers Determine the number of all four-digit natural numbers in decimal notation in which the digit 0 is not present, and each of the remaining nine numbers occurs at most once.
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