Factorial - practice problems
The factorial of the number n is the product of the first n natural numbers. For example 6! (we read 6 factorial) is 1*2*3*4*5*6 = 720.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 127
- Factorial divisible by 75
Find the least positive integer n such that n! is divisible by 75. - Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - 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? - Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people.
- Refrigerator 83310
How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other? - Married 83309
In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other? - Cancel variations
Evaluate the following expression with factorials: (45!-44!)/(44!) - Probability 82744
Ten books are placed randomly on one shelf. Find the probability that certain three books are placed next to each other. - Permutations 82516
From how many elements can we make 5040 permutations without repetition?
- Different 82447
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors? - SKMO Petra had written natural numbers from 1 to 9. She added two of these numbers, deleted them, and wrote the resulting sum instead of the summaries. She thus had eight numbers written down, which she managed to divide into two groups with the same product.
- Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have? - Parking 72644
How many ways can ten cars park side by side in a parking lot? - Assemble 70414
How many ways can we assemble five wagons when sand is in three wagons and cement in two?
- Classical 69634
Peter, Jano, Alice, and Rebecca attended a classical concert. How many different ways can they sit in the four free seats if Rebecca wants to sit with John? - Arrangements 68764
We have two identical blue balls and two identical red balls. We arrange them in a row in all ways. How many different arrangements are there? - Gradually 67284
Petra borrowed four books from the library at the beginning of the summer holidays. How many orders in which she could gradually read them? - Four-letter 67124
How many different four-letter words can we create from the letters of the word JAMA? - Word OPTICAL
Find the number of possible different arrangements of the letters of the word OPTICAL such that the vowels would always be together.
Marian obtained two different marks in one day. How many ways these marks can he get?Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
