Factorial - practice problems

Number of problems found: 107

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 went to a classical music 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
At the beginning of the summer holidays, Petra borrowed four books from the library. 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.
Different 65344
Marian obtained two different marks in one day. How many ways these marks did he can get?
Horizontally 64874
How many ways can an arranger display five different shampoos horizontally next to each other?
Sons
The father has six sons and ten identical, indistinguishable balls. How many ways can he give the balls to his sons if everyone gets at least one?
Triangle from sticks
Bob the boulder has many sticks of length 3,5 and 7 . He wants to form triangles each of whose edges consists of exactly 1 stick. How many non congruent can be form with the sticks.
Book Store
The Mabini Book Store (MBS) is reducing the prices of Mathematics books for promotion. The store has 6 Algebra books, 6 Geometry books, and 5 Statistics books to be arranged on a shelf. How many ways can these books be arranged on a shelf if books of the
Characters 63404
How many characters can we create from two commas and four dots?
Arrangements 63384
Determine the number of arrangements of these six elements: a, a, a, b, b, c.
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.
The flag
The flag should consist of 3 different colored stripes. Available colors: white, red, blue, green and yellow. Specify: A) number of all flags B) number of flags with a blue stripe C) number of flags with a blue stripe in the middle D) the number of flags
Indistinguishable 48981
How many ways can we build eight indistinguishable towers on an 8 × 8 board so that they don't endanger each other?
How many 13
How many ways can X³ y⁴ z³ be written without an exponent?
A department
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)?

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