# Combinatorics - practice problems - page 2 of 51

Combinatorics is a part of mathematics that investigates the questions of existence, creation and enumeration (determining the number) of configurations.It deals with two basic tasks:

How many ways can we select certain objects

How many ways can we arrange certain objects

#### Number of problems found: 1007

- A band

A band played an encore at 2 of its last 4 shows. Considering this data, how many of the band's next 14 shows would you expect to have an encore? - The marathon

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

Suppose you tossed a coin 12 times. The coin landed on heads 9 times and on tail 3 times. What is the probability of landing on tails?

- Library and gym

In a town, 7/8 of the population has a library card, and 3/4 has a gym membership. What fraction of the population has either a library card or a gym membership? - False positive, false negative

Suppose the likelihood of someone being allergic to cats is 1/1000 of the general population. A test to determine if you're allergic to cats has a false positive rate of 5%; that is, 5% of the time, the test will indicate incorrectly that you are allergic - Kenneth 2

Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents? - So far

So far on its tour, a band sold out 3 shows and did not sell out the other 3 shows. Considering this data, how many of the band's next 4 shows would you expect to be sold out? - 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.

- Probabilities

The bag has 10 green, 6 yellow, and 4 blue. What are the probabilities as a fraction, decimals, and percents? - Five couples

In how many ways can 5 couples arrange themselves in a row if they stay together? - 52 cards

A hand of five cards is dealt from a pack of 52 playing cards. How many different hands can be dealt that contain three aces? - Q10 - investigate

A nutritionist who investigates fruits reported that the average weight of a raspberry is 4.4 g with a standard deviation of 1.28 g. What is the probability that a randomly selected raspberry would weigh less than 3.1 grams? Let X represent the weight of - TF quiz

Gomer has to take a 5 question true/false quiz, but he hasn't studied. He will guess at each problem. In how many different ways is it possible to answer the quiz questions? How likely is it that he will get a score of 100%?

- Manufacturing company

It is established by the production manager of a manufacturing company that 2 out of every 20 units of a particular product are faulty. In a particular production hour, 8 units of the product were produced. Determine the probability that: (1) none of them - Diagonals

What is the number of diagonals of a decagon? - 3 sigma

Students' performance scores in a statistic test have a mean of 70 and a standard deviation of 4.0. The scores obtained can be modeled by a normal distribution. Find the probability that the score of a randomly selected student is i. more than 80 marks ii - Containers

One in eight containers is temporarily misplaced. A random sample of 12 containers is selected. What is the probability that 6 of these containers will be temporarily misplaced? - Bulb life

Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 675 and 900 hours.

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