Question

9) In a panel discussion with 3 industry employees, 2 government employees, and 1 association employee, how many ways can they be seated along a row…

a) …with no restrictions (each person can sit anywhere)?

b) …if the 3 industry employees must sit together (in any order) to the right of the others (also in any order)?

c) …if, prior to sitting, each of the industry employees is paired up with a partner and these pre-assigned pairs must stay together and sit beside one another?

Answer 1

a)

The number of possible seating arrangements are=

b)

The number of possible seating arrangements are=, first 3! is the arrangements of (2 government +1 association employees) and the next 3! is the arrangements of (3 industry employees)

c)

The number of possible seating arrangements are=, first 3 selections are the assigning pair to the industry empoloyees,3! is arrangements of 3 pairs and the next 2!'s are the arrangement among each pair.