6 people consists of 3 married couples. Each couple wants to sit with older partner on the left. Required:
a. How many ways can they be seated together in the row?
b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?

a. The first part asks for how many ways they can be seated together in a row. Therefore we want the permutations of the set of 6 people, or 6 factorial,

6! = 6 5

= 30 4

= 360 2 = 720 possible ways to order 6 people in a row

b. There are two cases to consider here. If the doctor were to sit in the left - most seat, or the right - most seat. In either case there would be 5 people remaining, and hence 5! possible ways to arrange themselves.

5! = 5 4

= 20 3

= 120 1 = 120 possible ways to arrange themselves if the doctor were to sit in either the left - most or right - most seat.

In either case there are 120 ways, so 120 + 120 = Total of 240 arrangements among the 6 people if the doctor sits in the aisle seat ( leftmost or rightmost seat )

c. With each husband on the left, there are 3 people left, all women, that we have to consider here.

3!  = 3 2 6 ways to arrange 3 couples in a row, the husband always to the left

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

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step-by-step explanation: