# Combinatorics - practice problems

#### Number of problems found: 428

- School group

There are 5 girls and 7 boys in the group. They sit in a row next to each other. How many options if no two girls sit next to each other. - Right key

The hostel has 4 rooms. The keys to each room are not numbered. Each of the four guests took one key. What is the probability that everyone took the right key? - In PE

In PE, students play a game where they do different exercises depending on the color of marble that Coach Forbes draws. Coach Forbes has a jar with 6 red marbles, 12 blue marbles, 16 purple marbles, 2 green marbles, and 4 yellow marbles. What is the proba - A box

A box contains 6 red balls, 5 blue, and 4 white balls. Find the probability of drawing a) red ball b) non-white ball. - ID tag

How many 3 digit ID tag can be made if: a) a digit cannot be used more than once b) the 1st digit must be five, and repetition of the others is not permitted. - There 8

There are 7 women and 5 men in a department. a) how many ways can a committee of 3 people be selected? b) how many ways can a committee of 2 men and 1 woman be selected? c) how many ways can a committee of at least 2 woman be selected (3 people total)? - Tic-tac-toe

In how many ways could 9 participants of the school round of five-in-a-row win the first three places? - Double six-six

What is the probability, that a player in the games of ludo will throw a double 6 twice . - Fruits

In the garden we want to plant 5 fruit trees, of which three are apple trees and two pears. How many different ways can we organize them? - The gems

The jeweler selects 4 gems for the ring. It has rubies, emeralds and sapphires. How many options does he have? - Syrups

In the shop they sell 3 types of syrups - apple, raspberry, orange. How many ways can you buy 4 bottles of syrup? - The six

The six boys are to be led up the hill by a two-seater lift. How many options are there? - Seedbeds

The father wants to plant 2 seedbeds of carrot and 2 seedbeds of onion. Use a tree chart to find how many different options for placing the seedbeds he has. - Honored students

Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them? - School parliament

There are 18 boys and 14 girls in the class. In how many ways can 3 representatives be elected to the school parliament, if these are to be: a) the boys themselves b) one boy and two girls - Two prizes

In a class of 15 pupils (7 boys and 8 girls), Teacher Mae is giving away a random prize. What is probability that both prizes are won by girls? - Soccer teams

Have to organize soccer teams. There are 3 age groups. How many different ways can you organize teams of ten for each age group? Is this a permutation or combination? - School committee

Seven students were elected to the school committee. In how many ways can become the President, Vice-President, Secretary, and Treasurer be selected? - Sum of fall dices

What is the probability that the sum of 9 will fall on a roll of two dice? Hint: write down all the pairs that can occur as follows: 11 12 13 14 15. . 21 22 23 24. .. . 31 32. .. . . . . . .. . 66, count them, it's the variable n variable m: 36, 63,. .. . - School club

Six boys and nine girls and a teacher played in the school club. What is the probability that they will point at the boy when they reproach?

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