Question

В 6 а классе в пятницу 6 уроков:математик, информатика, русский язык, английский язык, история, физкультура. Сколько всего можно составить вариантов расписания на пятницу? Сколько времени потратит завуч на запись всех вариантов, если известно, что на запись одного варианта у него уходит 30 с?

Answer 1

Всего вариантов по формуле
N = 6! = 6*5*4*3*2*1 = 720 вариантов.
Время на составление расписания - 30 с = 0,5 мин
0,5 мин * 720 =  360 мин = 6 час - ОТВЕТ.

Answer 2

Number of Possible Schedule Combinations

In the given scenario, there are 6 subjects: mathematics, computer science, Russian language, English language, history, and physical education. To determine the number of possible schedule combinations for Friday, we need to calculate the factorial of the number of subjects.

The factorial of a number is the product of all positive integers less than or equal to that number. For example, the factorial of 5 (written as 5!) is calculated as 5 x 4 x 3 x 2 x 1 = 120.

Therefore, the number of possible schedule combinations for Friday is 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

Time Spent by the Deputy Headmaster

Given that it takes the deputy headmaster 30 seconds to record one schedule variant, we can calculate the total time he will spend recording all the variants.

Since there are 720 possible schedule combinations, the deputy headmaster will spend 720 x 30 seconds = 21,600 seconds recording all the variants.

To convert this into minutes, we divide the total seconds by 60: 21,600 seconds ÷ 60 = 360 minutes.

Therefore, the deputy headmaster will spend 360 minutes recording all the schedule variants.

Please note that the above calculations assume that the deputy headmaster will record the schedule variants consecutively without any breaks or interruptions.