Question

2 почтальона должны разнести 10 писем по 10 адресам. Сколькими способами они могут распределить работу?

Answer 1

10÷2=5, 10÷2=5, 5×5=25

Answer 2

Calculating the Number of Ways to Distribute Mail

To calculate the number of ways two postal workers can distribute 10 letters to 10 addresses, we can use the concept of permutations.

Permutations are arrangements of objects in a specific order. The formula for permutations is given by:

nPr = n! / (n - r)!

Where: - n is the total number of items - r is the number of items to be arranged - ! denotes factorial, which is the product of all positive integers up to that number

Applying the Permutation Formula

In this case, we have 10 letters to be distributed to 10 addresses by 2 postal workers. This means each worker will distribute 5 letters to 5 addresses.

Using the permutation formula, we can calculate the number of ways the workers can distribute the letters:

For the first worker: - n = 10 (number of letters) - r = 5 (number of addresses) - nPr = 10! / (10 - 5)!

For the second worker: - n = 5 (remaining number of letters after the first worker's distribution) - r = 5 (remaining number of addresses after the first worker's distribution) - nPr = 5! / (5 - 5)!

Calculating the Total Number of Ways

To find the total number of ways both workers can distribute the letters, we multiply the number of ways for the first worker by the number of ways for the second worker.

Let's calculate the number of ways using the permutation formula and the given values.

For the first worker: - nPr = 10! / (10 - 5)! - nPr = 10! / 5! - nPr = (10 * 9 * 8 * 7 * 6 * 5!) / 5! - nPr = 10 * 9 * 8 * 7 * 6 - nPr = 30,240

For the second worker: - nPr = 5! / (5 - 5)! - nPr = 5! / 0! - nPr = 5! / 1 - nPr = 5 * 4 * 3 * 2 * 1 - nPr = 120

Total Number of Ways

To find the total number of ways both workers can distribute the letters, we multiply the number of ways for the first worker by the number of ways for the second worker.

Total number of ways = 30,240 * 120 = 3,628,800

Therefore, the two postal workers can distribute the 10 letters to 10 addresses in 3,628,800 ways.