Variations + permutations - practice problems
Number of problems found: 165
- Locker combination
Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly? - Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - A ferry
A ferry with a capacity of 10 people takes a group of 13 men and 7 women across a river. Find the number of ways in which the group may be taken across the if all women go on the first group.
- Three coins
In a game of chance where three coins are tossed, a player wins if two heads and a tail come up. What are the chances of this occurring? - 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? - Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people. - Probability - coin When tossing a coin 4 times in a row, what is the probability that a sign will come up 3 times?
- Celebration 83607
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 83538 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?
- 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 83340
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. - Different 82447
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors? - Possibilities 82372
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?
- Discovered 82210
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?
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