Two couples (Adam/Brenda and Carl/Darlene) have bought tickets for four adjacent seats to see a musical. In how many ways can the four people be seated if the couples do not sit together?

The correct answer is 8.

Step-by-step explanation:

Two couples have bought tickets for four adjacent seats to see a musical.

To find the number of ways can the four people be seated if the couples do not sit together. This is equivalent to finding total number of ways subtract number of ways they are sitting together.

Total number of ways four people can sit in four chairs are 4! = 24.

Number of ways the at least one of the couples sit together is 3! × 2 + 4= 16.

Total number of ways in which the couples do not sit together is

24 - 16 = 8.

We can even think this way (alternate way of thinking):

There are four chairs _ _ _ _.

For the first chair there are four possible options, i.e anyone can sit; then for the second chair there are only two possible options, i.e the other couple; for the third chair there is 1 option, i.e the spouse of the first person who sat on the first chair ; and for the last chair there is only one person left. Thus the number of ways are 4 × 2 × 1 × 1 = 8.

expression #3 is not equivalent. the others are.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)