Combinatorial number - practice problems - page 9 of 16

Number of problems found: 312

Classmate car selection
Karel wants to take some 15 classmates out of school after graduation. How many passengers does he have to choose if he has to fill the car (four-seater)?
Lottery prize probability
In the draw pole, five numbers out of 35 are drawn. The third prize is paid for three guessed numbers. What is the probability of winning the third prize if we submit a ticket with one of five numbers?
Four-element combinations
How many four-element combinations can we make from 10 elements?
Combination element calculation
How many elements is it possible to form twice as many second-class combinations as a fourth-class combination?
Delegation - b&g
There are 22 girls and nine boys in the class. How many ways can a delegation be created with three girls and one boy?
Student testing ways
There are 30 students in the class, three of whom will be tested. How many ways are possible if their order does not matter?
Point line determination
How many lines are determined by 5 points if three lie in one line?
Combination element count
From how many elements is it possible to create 120 second-class combinations?
Divide
How many different ways can three people divide seven pears and five apples?
Sick days
In Canada, there are typically 261 working days per year. There is a 4.9% chance of an employee taking a sick day. What is the probability an employee will use 17 OR MORE sick days in a year?
Fruits
The shop sells four kinds of fruits. How many ways can we buy three pieces of fruit?
Bouquets
The flower shop sells roses, tulips, and daffodils. How many different bouquets of five flowers can we make?
Twelve flowers
A florist has roses, tulips, daffodils, and carnations to use in flower arrangements. If she were to make an arrangement using 12 flowers, how many different combinations of these four types of flowers would be possible?
Pairs of socks
Ferdinand has twelve pairs of socks, and one sock is leaky. What is the probability of putting on a leaky sock?
Beads
How many ways can we thread four red, five blue, and six yellow beads onto a thread?
Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
Two groups
The group of 10 girls should be divided into two groups with at least four girls in each group. How many ways can this be done?
Graduation party
There were 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
Records
Records indicate 90% error-free. If eight records are randomly selected, what is the probability that at least two records have no errors?
Genetic disease
One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has three children. What is the probability of this family having one child who inher

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