Factorial - high school - practice problems
Number of problems found: 96
- Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - 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? - Indistinguishable 74294
We have eight compartments where we put three indistinguishable balls and two distinguishable ones. How many options do we have? - Assemble 70414
How many ways can we assemble five wagons when sand is in three wagons and cement in two? - 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? - 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. - 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 lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks? - Characters 63404
How many characters can we create from two commas and four dots? - School group
There are five girls and seven 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 flag - Indistinguishable 48981
How many ways can we build eight indistinguishable towers on an 8 × 8 board, so 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 seven women and five 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 one woman be selected? c) how many ways can a committee of at least two women be selected (3 people - Megapizza
Mega pizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion? - Permutations with repetitions
How many times can the input of 1.2.2.3.3.3.4 be permutated into four digits, three digits, and two digits without repetition? Ex: 4 digits = 1223, 2213, 3122, 2313, 4321. . etc 3 digits = 122.212.213.432. . etc 2 digits = 12, 21, 31, 23 I have tried the - Cups on the shelf
We should place two green, three red, and two yellow cups side by side on the shelf. a) How many different ways of setting up can arise? b) How many different ways of arranging can arise if cups of the same color stand side by side?
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