A game show has three doors labelled A,B, and C behind which there may or may not be a prize. A group of contestants are asked behind which doors they think there is a prize. The results are that 18 people choose A, 19 people choose B, 19 people choose C, 4 people choose A and B, 7 people choose A and C, 10 people choose B and C and 3 people choose all three. How many people are surveyed altogether

(18+19+19) - (4+7+10) + (3) = 38

To find the total number of people surveyed, we need to add up the number of people who choose each door individually and subtract the overlapping counts.

Given:
- 18 people choose A
- 19 people choose B
- 19 people choose C
- 4 people choose A and B
- 7 people choose A and C
- 10 people choose B and C
- 3 people choose all three (A, B, and C)

Let's calculate the total number of people surveyed:
18 (choose A) + 19 (choose B) + 19 (choose C) = 56

But we have counted some people more than once when considering the overlapping choices. So, we need to subtract those counts to avoid duplication.

- 4 (choose A and B) - 7 (choose A and C) - 10 (choose B and C) = -21

However, we also need to consider the 3 people who choose all three doors (A, B, and C). Since they are counted as choosing A, B, C individually as well as overlapping combinations, we need to add them back to avoid double subtraction.

-21 (subtracting overlapping counts) + 3 (choose all three) = -18

Finally, to eliminate the negative sign, we take the absolute value:

| -18 | = 18

Therefore, the total number of people surveyed is 18.

To find out how many people are surveyed altogether, we need to count the number of people who choose each door individually and those who choose multiple doors. Let's analyze the given information.

Given:
- 18 people choose door A
- 19 people choose door B
- 19 people choose door C
- 4 people choose both doors A and B
- 7 people choose both doors A and C
- 10 people choose both doors B and C
- 3 people choose all three doors (A, B, and C)

Now, let's break it down step by step to find the total number of people surveyed:

1. Start with the number of people who choose each door individually:
- Door A: 18 people
- Door B: 19 people
- Door C: 19 people

2. Account for those who choose multiple doors:
- People who choose both doors A and B: 4 people
- People who choose both doors A and C: 7 people
- People who choose both doors B and C: 10 people

3. Account for those who choose all three doors:
- People who choose all three doors (A, B, and C): 3 people

Now, let's add up the numbers:

18 (Door A) + 19 (Door B) + 19 (Door C) - 4 (A and B) - 7 (A and C) - 10 (B and C) + 3 (A, B, & C)

Simplifying that expression:

18 + 19 + 19 - 4 - 7 - 10 + 3 = 38

Therefore, the total number of people surveyed is 38.