Permutations without repetition n=42 result

The calculator computes the number of permutations of n elements. The 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 repetitions are not allowed. There are n! (n factorial) ways of arranging n objects into an ordered sequence.

Calculation:

P (n) = n! n = 42 P (42) = 42! = 1.4050061177529 \times 1 0^{51}

The number of permutations: 1.4050061177529×10⁵¹

1405006117752879898543142606244511569936384000000000

A bit of theory - the foundation of combinatorics

Permutations

A permutation is an ordered arrangement of all n elements of a set, where each element is used exactly once, the order matters, and no repetition is allowed.

P (n) = n (n - 1) (n - 2) . . . 1 = n!

Example: We have 4 books. In how many ways can we arrange them side by side on a shelf?

Foundation of combinatorics in word problems

Book shelf positions
How many positions are there to store three books on the shelf?
Football league
There are 16 teams in the football league. How many different sequences of results may occur at the end of the competition?
Disco
At the disco, there are 12 boys and 15 girls. In how many ways can we select four dancing couples?
Fourland - characters
In Fourland, they only have four letters F, O, U, and R, and every word has exactly four letters. No letter may be repeated in any word. Write all the words that can be written with them.
Natural numbers
How many natural numbers can we create less than 301 from the number 0,1,2,3,6,7?
Four-member team
There are 14 girls and 11 boys in the class. How many ways can a four-member team be chosen so that there are exactly two boys in it?
Digit sum
How many are three-digit numbers that have a digit sum of 6?
Team selection ways
Seven people need to be selected from the sports club, where 11 men and nine women. How many ways can we do this if seven women are on the team?
Seating pupils
We will work with a class in which there are 30 pupils, 40% of them are boys, the number of benches is 18. Determine the number of possibilities in the following tasks. 1) Determine in how many ways it is possible to select for a competition a trio of pup
Probability of picking
There are 5 chocolate, 3 cottage cheese, and 2 apricot croissants in the bag. Croissants are randomly selected in bags. What is the probability of drawing 1 chocolate, 1 cheese, and 1 apricot croissant without returning?
Number digit sum
How many numbers are less than 200, the digit sum of which is 6?
A bag 6
A bag contains 3 red marbles, 8 blue marbles, and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue?
Ways
There are 3 different roads from Lehota to Hradec and 4 different roads from Hradec to Buda. Determine the number of ways to choose a route from Lehota via Hradec to Buda and back, such that no road is used twice.
Triangles - segments
How many triangles can be formed with segments measuring 1 2/3 mm, 3/4 mm, and 2 1/2 mm?
A car license plate
A car licence plate consists of one letter (out of 26) and six digits. How many different plates can be formed if the letter is always in the second position and cannot be adjacent to a zero?