Select the correct answerThe thanksgiving banquet at No.2, Ritcher Street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. At the end of a banquet 19 people shake hands with other , some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. How many handshakes will there be in total?radio_button_unchecked342radio_button_unchecked171radio_button_unchecked180radio_button_unchecked162
Question
Select the correct answerThe thanksgiving banquet at No.2, Ritcher Street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. At the end of a banquet 19 people shake hands with other , some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. How many handshakes will there be in total?radio_button_unchecked342radio_button_unchecked171radio_button_unchecked180radio_button_unchecked162
Solution
The total number of handshakes can be calculated using the formula for combinations in a group, which is n(n-1)/2, where n is the number of people in the group.
In this case, there are 49 guests at the banquet, so the total number of handshakes would be 49(49-1)/2 = 1176.
However, the question states that only 19 people shake hands with others. This means that the total number of handshakes is not 1176, but rather the number of handshakes among these 19 people.
Using the same formula, the number of handshakes among these 19 people would be 19(19-1)/2 = 171.
So, the correct answer is 171.
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