# Permutations without repetition

The calculator calculates the number of permutations of n elements. Number of permutations is the number of ways to choose a sample of n elements from a set of n distinct objects where order does matter and repetition are not allowed. There are n! (n factorial) ways of arranging n objects into an ordered sequence.## Calculation:

$V_{k}(n)=(n−k)!n! n=10k=4V_{4}(10)=(10−4)!10! =6!10! =10⋅9⋅8⋅7=5040$

### The number of variations: 5040

# A bit of theory - the foundation of combinatorics

## Permutations

The permutation is a synonymous name for a variation of the nth class of n-elements. It is thus any n-element ordered group formed of n-elements. The elements are not repeated and depend on the order of the elements in the group.$P(n)=n(n−1)(n−2)...1=n!$

A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?

## Foundation of combinatorics in word problems

- Competition 69474

There are ten girls and seven boys in the dance group. Only one mixed couple is to go to the competition. How many are all possible pairs from which we can choose a pair for the competition? - Word OPTICAL

Find the number of possible different arrangements of the letters of the word OPTICAL such that the vowels would always be together. - Four-digit 65124

Please find out how many different four-digit numbers we can create from the digits 3 and 8 so that the two digits three and two digits eight are used in each four-digit number created. - A fair coin

A fair coin is tossed twice. Write down the set of possible outcomes. What is the probability of obtaining it? I. Exactly one head ii. No head - Page numbering

The book has 88 pages. How many times is the number 4 used for the book numbering? - Toys

3 children pulled 6 different toys from a box. How many ways can toys be divided, so each child has at least one toy? - Glass with icecream

We have six kinds of ice cream and five kinds of fruit. We put 3 cups of ice cream and two fruits into each glass. How many can unique decorated glasses be? - Individual 65004

In the computer game, you need to collect 5 objects in the room: a sword, a ring, a picture, a key, and a coin. It depends on the order in which we collect the individual objects. If the order is wrong, we will lose a life. How many are all in order? - Olympics

How many ways can six athletes be placed on the podium at the Olympics? Depend on the color of the metal. - Permutations

How many 4-digit numbers can be composed of numbers 1,2,3,4,5,6,7 if: and the digits must not be repeated in the number b, the number should be divisible by five, and the numbers must not be repeated c, digits can be repeated - Kenneth 2

Kenneth has 100 pennies, 20 nickels, 10 dimes, and 4 quarters. How many ways can he choose coins that total 25 cents? - Hockey match

The hockey match ended with a result of 3:1. How many different storylines may the match have? - Classroom

Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys - Five-digit 66894

Create all five-digit numbers in ascending order from three, four, and two zeros. - Probability 72324

We used the digits 2, 3, 4, 5, and 7 when entering the PIN code, and we only used each digit once. What is the probability that someone will guess our PIN code on the first try? - Digits

How many natural numbers greater than 4000 are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many will the number of natural numbers be less than 4000, and can the numbers be repeated?

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