Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 4 - Objective Problem 3
In a conference of scientists every scientist handshakes with exactly two other scientists. In how many ways can this happen?
This problem is a part of Tessellate S.T.E.M.S (2019)
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1 solution
When the 9 scientists arrive at the conference, they find tables in the conference room arranged in one of the following ways:
1) one large round table,
2) two round tables - one small table with 3 seats and one with 6 seats,
3) two round tables - one table with 4 seats and one with 5 seats,
4) three round tables with 3 seats each.
Each scientist finds an empty seat, sits and shakes hands with the neighbour to the left and to the right:
for the table arrangement 1), the number of ways to shake hands is 9!/9/2=20160,
for the table arrangement 2), the number of ways to shake hands is 9!/3!/(9-3)! ∗ 6!/6/2 =5040,
for the table arrangement 3), the number of ways to shake hands is 9!/4!/(9-4)! ∗ 5!/5/2 ∗ 4!/4/2=4536,
for the table arrangement 4), the number of ways to shake hands is 9!/(3! ∗ 3! ∗ 3!)/3!=280.
So the total number of ways to shake hands is 20160+5040+4536+280= 3 0 0 1 6 .