Take a look at a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place?

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Luis Sullivan · Accepted Answer

The two participants in a handshake are the only ones who define it. Therefore, among 20 people, there are as many handshakes as groups of two. The binomial is defined as the number of unorder groups of two among 20 different objects.(202)=20⋅192!=190We could have used a different approach to achieve the same outcome. This is how binomials are introduced in the book.Every person will shake hands with each of the remaining 19 people. By the basic principle of counting, this gives us&amp;nbsp;20⋅19&amp;nbsp;people. But this way, the participants of the handshake were ordered, that is we counted &quot;Frank shakes hands with Amy&quot; and &quot;Amy shakes hands with Frank&quot; as two different handshakes. So the count is actually half of the first number.20⋅192=190

Mr Solver · Accepted Answer

Step 1: To find the number of handshakes that take place in a group of 20 people, we can use the formula for the sum of the first n natural numbers. In this case, n=19, since one person cannot shake hands with themselves.The formula for the sum of the first n natural numbers is given by:∑k=1nk=n(n+1)2Step 2: Substituting n=19 into the formula, we get:∑k=119k=19(19+1)2=19×202=190Therefore, there would be 190 handshakes taking place among 20 people.

Eliza Beth13 · Accepted Answer

Answer:190Explanation:Let&#039;s consider the first person in the group. This person can shake hands with 19 other people in the group (excluding themselves).The second person can shake hands with the remaining 18 people (excluding themselves and the person they already shook hands with).Similarly, the third person can shake hands with the remaining 17 people, and so on.We can see that the number of handshakes decreases by one for each person in the group.Therefore, the total number of handshakes H can be calculated using the formula:H=19+18+17+…+2+1We can rewrite this formula using summation notation as:H=∑n=119nNow, let&#039;s calculate the value of H:H=∑n=119n=19·(19+1)2=19·202=190Thus, there will be 190 handshakes taking place among the group of 20 people.

Nick Camelot · Accepted Answer

To solve the problem, we can use a combination formula to calculate the number of handshakes. The combination formula is given by:C(n,r)=n!r!(n−r)!where C(n,r) represents the number of combinations of r items chosen from a set of n items, and n! denotes the factorial of n.In this case, we have a group of 20 people, and we want to find the number of handshakes. Each person shakes hands with every other person, so we need to choose 2 people at a time from the group of 20.Using the combination formula, we have:C(20,2)=20!2!(20−2)!Simplifying further:C(20,2)=20!2!·18!Since 2!=2, we can substitute this value:C(20,2)=20!2·18!Now, let&#039;s calculate the factorial:C(20,2)=20·19·18!2·18!Simplifying the expression:C(20,2)=20·192C(20,2)=190Therefore, there are 190 handshakes that take place among the 20 people in the group.

Consider a group of 20 people. If everyone shakes hands with everyone else, how

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