Answer:
( E ) 0
Step-by-step explanation:
Solution:-
- There can be two ways in solving this question. Either we lay-out a map of every person ( Alan, Bella, Claire, Dora, and Erik ) shaking hands with each other.
- We will use an intuitive way of tackling this problem.
- We have a total of 5 people who greeted each other at the party.
- Each of the 5 people shook hands exactly " once "! We can give this a technical term of " shaking hands - without replacement ".
- We will define our event as shaking hands. It takes 2 people to shake hands.
- We will try to determine the total number of unique "combinations" that would result in each person shaking hands exactly one time.
- We have a total of 5 people and we will make unique combinations of 2 people shaking hands. This can be written as:
5C2 = 10 possible ways.
- So there are a total of 10 possible ways for 5 people to greet each other exactly once at the party.
- We are already given the data for how many handshakes were made by each person as follows:
Name Number of handshakes
Alan 1
Bella 2
Claire 3
Dora 4
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Total 10
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- So from the data given. 10 unique hand-shakes were already done by the time it was " Eriks " turn to go and greet someone. This also means that Erik has already met all 4 people in that party. So he doesn't have to approach anyone to shake hands and know someone. He is already been introduced to rest of 4 people in the group.
Answer: Erik does not need to shake hands with anyone! He is known and greeted rest of the 4 people on the group.
