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

Phone numbers
How many 9-digit telephone numbers can be formed from the digits 0, 1, 2, ..., 9 if no digit is repeated?
N-gon
How many diagonals does a convex 30-gon have?
Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)?
School trip
The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number)
Playing cards
In how many possible ways can 6 playing cards be shuffled?