Question

Скількома способами можна розкласти 8 різних поштових листів по восьми різним конвертам?

Answer 1

Ответ:

40320

Объяснение:

8!=8*7*6*4*3*2*1=40320

Answer 2

Ways to Arrange 8 Different Letters in 8 Different Envelopes

To calculate the number of ways to arrange 8 different letters in 8 different envelopes, we can use the concept of permutations. In mathematics, a permutation is an arrangement of objects in a specific order. The formula to calculate the number of permutations is given by:

nPr = n! / (n - r)!

Where: - n is the total number of items - r is the number of items taken at a time - ! denotes factorial, which is the product of all positive integers up to that number

Calculation

In this case, we have 8 different letters and 8 different envelopes, so we want to find the number of ways to arrange all the letters in the envelopes, which is a permutation of 8 items taken 8 at a time.

Using the formula, we get:

8P8 = 8! / (8 - 8)!

8P8 = 8! / 0!

Result

Calculating 8 factorial (8!) gives us:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

And since 0! is defined as 1, we have:

8P8 = 40,320 / 1 = 40,320

So, there are 40,320 ways to arrange 8 different letters in 8 different envelopes. [[1]]