# Combinatorics - math word problems

#### Number of problems found: 420

• Bridge cards
How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
• Two doctors
Doctor A will determine the correct diagnosis with a probability of 93% and doctor B with a probability of 79%. Calculate the probability of proper diagnosis if both doctors diagnose the patient.
• The three
The three boys Adam, Boris and Cyril are to be taken on a two-seater ski lift. How many different removal options are there? What would it be like if four boys or five were to be taken away?
• Bouquets
In the flower shop they sell roses, tulips and daffodils. How many different bouquets of 5 flowers can we made?
• Test
The teacher prepared a test with ten questions. The student can choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers all correctly. c
• Fruits
In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?
• Numbers
How many different 3 digit natural numbers in which no digit is repeated can be composed of digits 0,1,2?
• Six questions test
There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
• Covid-19
Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
• Three wagons
I have 6 different people (A, B, C, D, E, F), which I have to place into 3 wagons, if it depends on who will board. How many options are there?
• Air draft
The numbers 1,2,3,4,5 are written on five tickets on the table. Air draft randomly shuffled the tickets and composed a 5-digit number from them. What is the probability that he passed: and, the largest possible number b, the smallest possible number c, a
• Internet anywhere
In school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) At least 6 students have access to the internet
• Probability
How probable is a randomly selected three-digit number divisible by five or seven?
• Crimson Lynx
Captain Emily has a ship, the H. M. S Crimson Lynx. The ship is five furlongs from the dread pirate Umaima and her merciless band of thieves. If her ship hasn't already been hit, Captain Emily has probability 3/5 of hitting the pirate ship. If her ship ha
• Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because exactly one of the
• Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
• A bag
A bag contains 9 blue marbles and 1 green marble. What is the probability of drawing a blue marble followed by a green marble, without replacing the first marble before drawing the second marble.
The voltage station is day changing the master password, which consists of three letters. The code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9 if
• Two dice
We roll two dice. What is the probability that the sum of the falling numbers is greater than 3?
• Inverted nine
In the hotel Inverted Nine, each hotel room number is divisible by 6. How many rooms can we count with the three-digit number registered by digits 1,8,7,4,9?

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