Solution:

To find the probability that the certain married couple serves together or not at all, we need to consider two cases:

Case 1: The married couple serves together in the committee
In this case, we need to choose 3 more people from the remaining 7 people (excluding the married couple). The number of ways to do this is:

C(7,3) = 35

Case 2: The married couple does not serve in the committee
In this case, we can choose any 5 people from the remaining 7 people (excluding the married couple). The number of ways to do this is:

C(7,5) = 21

Total number of ways to choose a committee of 5 people from a group of 9 people is:

C(9,5) = 126

Therefore, the probability that the certain married couple serves together or not at all is:

(35 + 21) / 126 = 4/9

Hence, the correct option is (c).

Solution:
To find the probability that a certain married couple serve together or not at all, we need to calculate the total number of ways of choosing a committee of 5 people from 9 and subtract the number of ways of choosing a committee of 5 people such that the married couple serves together.

Total number of ways of choosing a committee of 5 people from 9 = 9C5 = 126

Number of ways of choosing a committee of 5 people such that the married couple serves together:

We can treat the married couple as a single entity and choose 4 more people from the remaining 8 people. The number of ways of doing this is 8C4.

Also, the married couple can serve in two ways, either the husband can serve or the wife can serve. So, we need to multiply 8C4 by 2.

Therefore, the number of ways of choosing a committee of 5 people such that the married couple serves together = 2 * 8C4 = 2 * 70 = 140

Number of ways of choosing a committee of 5 people such that the married couple does not serve together:

Total number of ways of choosing a committee of 5 people from 9 = 126

Number of ways of choosing a committee of 5 people such that the married couple serves together = 140

Therefore, the number of ways of choosing a committee of 5 people such that the married couple does not serve together = 126 - 140 = -14

Since the number of ways cannot be negative, we conclude that there are no ways of choosing a committee of 5 people such that the married couple does not serve together.

Therefore, the probability that a certain married couple serve together or not at all is:

Probability = Number of ways of choosing a committee of 5 people such that the married couple serves together / Total number of ways of choosing a committee of 5 people from 9

Probability = 140 / 126 = 20 / 18 = 10 / 9

Probability that a certain married couple serve together or not at all = 1 - Probability that the married couple does not serve together

Probability that the married couple does not serve together = 0

Therefore, Probability that a certain married couple serve together or not at all = 1 - 0 = 1

So, the probability that a certain married couple serve together or not at all is 1, which means that the married couple will always serve together in any committee of 5 people chosen from 9 people.