Permutations - practice problems - page 2 of 13
Number of problems found: 259
- 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) - A lottery
In a lottery, a person chooses four different natural numbers at random from 1 to 10, and if these four numbers match the four numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? (Th - Different balls
We have four different boxes and three identical balls. Place the marbles in these boxes so that the boxes can contain one, two, three or none. How many other locations are there? - Numbers 6D Find out how many natural six-digit numbers exist whose digit sum is four.
- Wardrobe code Lucia has a lock on her wardrobe that opens with a 4-digit code (such as 0000, 0089, or 9123). Lucia forgot her code. But she knows that the sum of all four digits of her code is 4. How many such codes are there?
- 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? - Refrigerator, lemonades
How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other? - Probability - shelf
Ten books are placed randomly on one shelf. Find the probability that certain three books are placed next to each other. - Permutations 82516
From how many elements can we make 5040 permutations without repetition?
- Different 82447
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors? - Play match
A hockey match played for three periods ended with a score of 2:3. How many possibilities are there on how the given thirds could have been completed? - Choices 82334 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?
- Dance party
At the dance party, the organizer discovered that 168 different dance pairs could be formed from girls and boys. How many boys are there at the dance if there are 12 girls? - Four-digit 82023 How many four-digit numbers are there in which there are at least three eights
- Repetition: 82003
Calculate how many different monograms (short name and surname) I can make from the letters A, E, M, Z, and K. a) with repetition: b) without repetition: - Position 81987 Find a number with six digits. If you put the last digit before the first, you get a new number that is five times larger. The digits between must not change their position.
- 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 - Participated 81728 The school volleyball tournament was played on a one-on-one basis. One match lasted 15 minutes, and 3 hours and 45 minutes were played. Calculate how many teams participated.
- Probability 81679 What is the probability that a roll of three dice will result in a number less than 7?
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