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Question:

In how many different orders can 3 married couples be seated in a row of 6 chairs:?

under the following conditions:a. Anyone may sit in any chairb. Men must occupy the first and last chairsc. Men must occupy the first three chairs and women must occupy the last three chairsd. Everyone must be seated beside his or her spouseIs this a combination or permutation? or neither?

Answer:

a. 6! = 720. 6 ways to choose the first person, 5 to choose the next, etc. b. 3! * 4 * 3! = 144. Choose 1 of 3 men for the first chair, 1 of 2 men for the last. Choose 1 of 4 seats for the last man. Choose 1 of 3 women for the first remaining chair, 1 of 2 for the second remaining chair. c. 3! * 3! = 36. Choose 1 of 3 mean for the first chair, 1 of 2 men for the second. Choose 1 of 3 women for the fourth chair, 1 of 2 women for the fifth. d. 3! * 2^3 = 48. Choose 1 of 3 couples for the first two seats, 1 of 2 orders for that couple. Choose 1 of 2 couples for the third and fourth seats, 1 of 2 orders for that couple. Choose 1 of 2 orders for the third couple. These are all permutations.
Sep 30, 2017
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Sep 30, 2017

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