Question

Среди пассажиров, едущих в вагоне, шло оживленное обсуждение четырех журналов. Оказалось, что каждый выписывает два журнала, причем каждая из возможных комбинаций двух журналов выписывается ОДНИМ человеком. Сколько человек было в этой группе? 1) 6 пассажиров 2) 8 пассажиров 3) 5 пассажиров 4) 9 пассажиров

Answer 1

Ответ 1) 6 пассажиров

обозначим журналы буквами АВСD
1 пассажир - A и B
2 - А и С
3 - А и D
4 - В и С
5 - В и D
6 - C и D
больше вариантов нет

Answer 2

Problem Analysis

In the given scenario, there is a lively discussion among the passengers in a train carriage about four magazines. It is discovered that each passenger subscribes to two magazines, and each possible combination of two magazines is subscribed to by exactly one person. We need to determine the number of people in this group.

Solution

Let's consider the number of people in the group as 'x'. Since each person subscribes to two magazines, there will be a total of '2x' magazine subscriptions in the group.

To find the number of unique magazine combinations, we can use the formula for combinations: nCr = n! / (r!(n-r)!), where 'n' is the total number of magazines and 'r' is the number of magazines in each combination.

In this case, there are four magazines, so 'n' is 4, and 'r' is 2. Therefore, the number of unique magazine combinations is:

nCr = 4! / (2!(4-2)!) = 4! / (2!2!) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6

Since each combination is subscribed to by exactly one person, the number of magazine subscriptions '2x' is equal to the number of unique magazine combinations, which is 6.

Therefore, we can solve the equation '2x = 6' to find the value of 'x'.

Calculation

Let's solve the equation '2x = 6' to find the value of 'x':

2x = 6 Divide both sides by 2: x = 6 / 2 x = 3

Answer

Therefore, there were 3 passengers in this group.