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If there were no 'four person' constraint, the six people could be accommodated in $4^6=4096$ ways. however, this number includes combinations with 5 or 6 people in one room, which should be excluded.
Oct 15, 2014 · If the rooms were large enough to accommodate all $6$ people, there would be $4^6$ possible arrangements. However, $4$ of those arrangements have all $6$ in one room, and some have $5$ in one room and $1$ in another; all of those must be subtracted from $4^6=4096$.
Free Group Combinations Calculator - Given an original group of certain types of member, this determines how many groups/teams can be formed using a certain condition. This calculator has 3 inputs.
- The Handshake Problem
- Small Groups
- Groups of Four People
- Larger Groups
- Creating A Formula For The Handshake Problem
- An Interesting Aside: Triangular Numbers
- Related Articles
- Questions & Answers
The handshake problem is very simple to explain. Basically, if you have a room full of people, how many handshakes are needed for each person to have shaken everybody else's hand exactly once? For small groups, the solution is quite simple and can be counted fairly quickly, but what about 20 people? Or 50? Or 1000? In this article, we will look at ...
Let's start by looking at solutions for small groups of people. The answer is obvious for a group of 2 people: only 1 handshake is needed. For a group of 3 people, person 1 will shake the hands of person 2 and person 3. This leaves person 2 and 3 to shake hands with each other for a total of 3 handshakes. For groups larger than 3, we will require a...
Suppose we have four people in a room, whom we shall call A, B, C and D. We can split this into separate steps to make counting easier. 1. Person A shakes hands with each of the other people in turn—3 handshakes. 2. Person B has now shaken hands with A but still needs to shake hands with C and D—2 more handshakes. 3. Person C has now shaken hands w...
If you look closely at our calculation for the group of four, you can see a pattern that we can use to continue to work out the number of handshakes needed for different-sized groups. Suppose we have npeople in a room. 1. The first person shakes hands with everybody in the room except for himself. His total number of handshakes is, therefore, one l...
Our method so far is great for fairly small groupings, but it will still take a while for larger groups. For this reason, we will create an algebraic formula to instantly calculate the number of handshakes required for any size group. Suppose you have npeople in a room. Using our logic from above: 1. Person 1 shakes n - 1 hands 2. Person 2 shakes n...
If you look at the number of handshakes required for each group, you can see that each time the group size increases by one, the increase in handshakes is one more than the previous increase had been. i.e. 1. 2 people = 1 2. 3 people = 1 + 2 3. 4 people = 1 + 2 + 3 4. 5 people = 1 + 2 + 3 + 4, and so on. The list of numbers created by this method, ...
Question:A meeting was attended by some people. Before the start of the meeting, each of them had handshakes with every other exactly once. The total number of handshakes thus made was counted and found to be 36. How many persons attended the meeting based on the handshake problem? Answer:Setting our formula equal to 36 we get n x (n-1)/2 = 36. n x...
Dec 15, 2023 · However, the surprising answer is that you only need 23 people in the room. With 23 people in the room, there is a 50.7% chance that at least two of those people share a birthday. Don't believe me? Read on to find out why.
Nov 28, 2018 · Maximum Occupancy A hotel has four vacant rooms. Each room can accommodate a maximum of four people. In how many ways can six people be accommodated in the four rooms? There seems to be lots of different configurations, e.g., zero people in rooms 1 and 2, two in room 3, and four in room 4.
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The number of handshakes when 4 people shake hands with each other can be calculated using the combination formula in mathematics. The combination of 4 people taken 2 at a time (a pair for a handshake) is 6, hence there will be 6 handshakes. Explanation:
