under the following conditions:
a. Anyone may sit in any chair
b. Men must occupy the first and last chairs
c. Men must occupy the first three chairs and women must occupy the last three chairs
d. Everyone must be seated beside his or her spouse
Is this a combination or permutation? or neither?
a. Anyone may sit in any chair
b. Men must occupy the first and last chairs
c. Men must occupy the first three chairs and women must occupy the last three chairs
d. Everyone must be seated beside his or her spouse
Is this a combination or permutation? or neither?
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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.
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.