Combinatorics - practice problems
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: 1026
- One ticket 2
In a lottery, 10000 tickets are sold and ten prizes are awarded. What is the probability of not getting a prize, if you buy one ticket? - Pair of dice
In a throw of a pair of dice, find the probability of the same number on each die. - A restaurant’s
A restaurant’s menu has 3 appetizers, 3 mains and 2 desserts. In how many way can a 3-course meal be ordered? - The marbles
There are 10 red marbles, 6 green marbles, and 4 blue marbles in a box. What is the probability of picking the next red marble?
- Two coins
Two coins are tossed simultaneously. What is the probability of getting (i) At least one head? (ii) At most one tail? (iii) A head and a tail? - 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? - 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? - 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?
- Student examination
How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students?
- Selecting a group How many ways can a teacher select a group of 3 students to sit in the front row if the class has 13 students?
- A single A single, standard number cube is tossed. What is the probability of getting a number greater than 3?
- Pet store 2
A pet store is having a prize giveaway. The spinner shows the type of toy a customer can win for their pet. If a customer spins the spinner and it lands on a cat, they will win a free cat toy. If the spinner is spun 540 times throughout the day, about how - Assume 2
Assume you are working with a standard six-sided die. What is the probability of rolling the die once and obtaining a 5 and then rolling the die again and obtaining a 2? (input 3 numbers after the decimal, do not round). Report probability as a proportion - A fair 2 A fair die is thrown two times. What is the probability that the sum of the score is almost 8?
- The probability 2
The probability that an adult possesses a credit card is 0.71. A researcher selects two adults at random. The probability (rounded to three decimal places) that the first adult possesses a credit card and the second adult does not possess a credit card is - Five roommates Five roommates will move into a house with four bedrooms: one double room and three single rooms. The five roommates propose that they draw names to determine the order in which they pick the bedrooms, assuming that the first three names drawn will choose
- Testing students
Giving a test to a group of students, the grades and gender are summarized below. Grades and Gender ; A; B ; C ; Total Male; 20; 6; 19 ; 45 Female ; 17; 18; 13; 48 Total; 37; 24; 32; 93 If one student is chosen at random, a) Find the probability that the - Richard Richard is conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number?
- Ruben
Ruben owns a restaurant. He likes to keep track of everything customers are buying. His top 3 sellers are sandwiches, salads, and pizza. He knows that 1/3 of his customers buy a sandwich, 1/2 buy a salad, and 1/4 buy a pizza. What fraction of customers bu
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