## Task 2 - 220822

In a survey, 50 pioneers of a school answered the following questions on a questionnaire:

|  |  | Yes | No |
| :--- | :--- | :---: | :---: |
| (A) | Did you participate in a company summer camp this summer? | o | o |
| (B) | Did you participate in the school's summer activities this summer? | o | o |
| (C) | Did you travel with your parents this summer? | o | o |

Subsequently, the answers were counted multiple times. In the first count, only the answers to question (A) were considered for all questionnaires. This resulted in exactly 20 pioneers answering Yes. Then, in a second count, only the answers to question (B) were considered for all 50 questionnaires, and so on, as specified in the following table:

| Count No. | Counted Answers | Obtained Number |
| :---: | :--- | :---: |
| 1 | (A) Yes | 20 |
| 2 | (B) Yes | 25 |
| 3 | (C) Yes | 30 |
| 4 | (A) Yes and (B) Yes | 8 |
| 5 | (B) Yes and (C) Yes | 12 |
| 6 | (A) Yes and (C) Yes | 10 |
| 7 | (A) Yes and (B) Yes and (C) Yes | 3 |

From these counting results, the number of pioneers who

a) did not participate in any of the three types of summer activities,

b) participated in exactly one of these types,

c) participated in a company summer camp but not in the school's summer activities,

d) used at least one of the options to participate in a company summer camp or travel with their parents.

Enter the sought answers in the following table! Provide the calculations or reasoning that support your answers!

| Task | Sought Answers | Obtained Number |
| :---: | :--- | :--- |
| a) | Never Yes |  |
| b) | Exactly once Yes |  |
| c) | (A) Yes and (B) No |  |
| d) | (A) Yes or (C) Yes or both |  |
The sought entries can be found through the following calculation steps:

| Statement  No. | Sought Answers | Conclusion from Statement No. | Calculation of the Number |
| :--- | :--- | :--- | :--- |
| 8 | (A)Yes, (B)Yes, (C)No | 4,7 | $8-3=5$ |
| 9 | (A)Yes, (B)No, (C)Yes | 6,7 | $10-3=7$ |
| 10 | (A)No, (B)Yes, (C)Yes | 5,7 | $12-3=9$ |
| 11 | (A)Yes, (B)No, (C)No | $1,7,8,9$ | $20-3-5-7=5$ |
| 12 | (A)No, (B)Yes, (C)No | $2,7,8,10$ | $25-3-5-9=8$ |
| 13 | (A)No, (B)No, (C)Yes | $3,7,9,10$ | $30-3-7-9=11$ |
| Task |  |  |  |
| a) | Never Yes | $7, \ldots, 13$ | $50-3-5-7-9-5-8-11=2$ |
| b) | Exactly once Yes | $11,12,13$ | $5+8+11=24$ |
| c) | (A)Yes and (B)No | 9,11 | $7+5=12$ |
| d) | (A)Yes or (C)Yes or both | $7, \ldots, 11,13$ | $3+5+7+9+5+11=40$ |