Yukio and his 5 friends want to keep in touch during winter vacation. If they each speak to everyone in their group once during the week, how many calls will be made?
This is the same as the hand-shake problem.
N people talked to N-1 people. But each call involves two people, so the number of calls is N(N-1)/2.
To determine the total number of calls that will be made, we need to calculate the number of unique pairs within the group of Yukio and his 5 friends.
Since Yukio and his friends want to speak to everyone in their group once during the week, each person will talk to the other five members once. This means that for each person, there will be five calls made.
To calculate the total number of calls, we multiply the number of people (including Yukio) by the number of calls made by each person:
Total number of calls = number of people × number of calls made by each person
In this case, there are six people (Yukio and his five friends), and each person makes five calls.
Total number of calls = 6 × 5 = 30
Therefore, there will be a total of 30 calls made during the winter vacation.