1. Suppose that eight people are sitting down at two square tables. Each table i

Question

1. Suppose that eight people are sitting down at two square tables. Each table is set up so that the seats are in the four cardinal directions (that is, North, South, East, and West.)

(a) How many different arrangements of the eight people into seats are there?

(b) How many different ways can the eight people divide between the two tables (ignoring positions at each table)?

(c) Suppose that A takes the North chair at table 1, and B then chooses to sit at table 2. How many different arrangements of the eight people are possible?

(d) Now suppose that the eight people are made up of four couples, and each couple sits across a table.(That is, North-South or East-West.) How many arrangements of the eight people will satisfy this requirement?

(e) Again assume that there are four couples, but now suppose that we never seat members of a couple at the same table. How many arrangements would satisfy this constraint?

Explanation / Answer

a) 8C4 * 4! * 4! * 2 = 80640

b) 8C4 = 1680

(c) (6c3) * 3! *4! =2880

d) (4c2) *2!* 2! = 24

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