# Variations - practice problems

#### Number of problems found: 286

- The marathon

Twelve athletes are joining the Topolcany Marathon Event. How many ways can the first, second, and third placers be chosen? - 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 bag 6

A bag contains 3 red marbles, 8 blue marbles, and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue?

- 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? - 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 83310

How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other?

- Married 83309

In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other? - Cancel variations

Evaluate the following expression with factorials: (45!-44!)/(44!) - Probability 82744

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? - 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: - Consecutively numbers

How many ways are there to arrange the numbers 3, 2, 15, 8, and 6 so that the even numbers are arranged in ascending order (not necessarily consecutively)?

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