Question

There are 20 persons at a party. Each person shakes hands with some of the persons at the party. Let K be the number of persons who shook hands with odd number of persons. What is a possible value of K?

A. 19
B. 1
C. 20
D. All of the above

Answer 1

In this problem, we need to determine the possible values of K, which represents the number of people who shook hands with an odd number of individuals at the party. Therefore, the possible values of K are A. 19, B. 1, C. 20, and D. All of the above.

Step-by-step explanation:

In this problem, we need to determine the possible values of K, which represents the number of people who shook hands with an odd number of individuals at the party. Since each person shakes hands with some of the others, we can consider each person as an outcome. Let's use some examples to illustrate the possible values of K:

1. If each person shook hands with an even number of individuals, then K would be 0.
2. If 19 people shook hands with an even number of individuals, and one person shook hands with an odd number of individuals, then K would be 1.
3. If each person except for one shook hands with an odd number of individuals, and that one person shook hands with an even number of individuals, then K would be 19.
4. If each person at the party shook hands with an odd number of individuals, then K would be 20.

Therefore, the possible values of K are A. 19, B. 1, C. 20, and D. All of the above.