Question

сколько различных четных пятизначных чисел можно составить из цифр 1,2,3,4,5,6, если каждая цифра содержится в записи числа только один раз?

Answer 1

так как 6 возможных вариантов, => 6*5*4*3*2=720 (вроде так нас учили)

 

Answer 2

Calculating the Number of Even Five-Digit Numbers

To calculate the number of different even five-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with each digit occurring only once, we can follow these steps:

1. Identify the Even Digits: Identify the even digits in the given set of numbers. 2. Count the Possibilities: Calculate the number of ways these even digits can be arranged to form a five-digit number.

Identifying the Even Digits

The even digits in the given set of numbers (1, 2, 3, 4, 5, 6) are 2, 4, and 6.

Counting the Possibilities

To form a five-digit number, the first digit cannot be 0. Therefore, the first digit can be chosen in 5 ways (since 0 is not included). The remaining 5 digits can be arranged in 5! (5 factorial) ways.

Therefore, the total number of different even five-digit numbers that can be formed is given by: \[ 5 \times 5! \]

Conclusion

The total number of different even five-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with each digit occurring only once, is 600. This is calculated as 5 (choices for the first digit) multiplied by 5! (arrangements of the remaining digits).

I hope this helps! If you have any further questions, feel free to ask.