Make sure to explain yourself in your responses to the following questions to ensure you get full credit.
1) During the handshaking activity in a class, Joe claimed: "The total number of handshakes reported by everyone must add up to an even number." When asked to justify his statement, Joe said, "It is because there is an even number of people in the class." Is Joe's claim correct? Is his reason for the claim correct? Why or why note?
2) A group of friends meet up at a party. Some of them greet each other with fist bumps. Determine if the following numbers of fist bumps are possible. If so, describe a procedure of the fist bumbs. If not, explain why not.
a) In a group of 3, the desired fist bump sequence is (1,1,1).
b) In a group of 4, the desired fist bump sequence is (3,3,2,2).
c) In a group of 5, the desired fist bump sequence is (5,2,2,1,0).