The Venn Diagram is shown at the end of the answer.
Then the amounts are given as follows:
- History or did not take dance: 1769.
- History or math, but not dance: 917.
- Dance and Math, but not history: 343.
- History, Dance or Math: 2153.
How to fill the Venn Diagram?
The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.
286 students took all three courses, hence:
V = 286.
629 students were taking history and dance, hence:
VI + V = 629
VI + 286 = 629
VI = 343.
605 students took history and math, hence:
IV + V = 605
IV = 605 - 286
IV = 319.
604 students took dance and math, hence:
II + V = 604
II = 318.
1236 students took dance, hence:
III + II + VI + V = 1236
III + 318 + 343 + 286 = 1236
III = 1236 - (318 + 343 + 286)
III = 289
1295 students took math, hence:
VIII + IV + V + VI = 1295
VIII + 319 + 286 + 343 = 1295
VIII = 1295 - (319 + 286 + 343)
VII = 347
1174 students took history, hence:
I + II + IV + V = 1174
I + 318 + 319 + 286 = 1174
I = 1174 - (318 + 319 + 286)
I = 251
Then the number of students who took at least one of the subjects is of:
251 + 318 + 289 + 319 + 286 + 343 + 347 = 2153.
The number of students who took none of the subjects is of:
2401 - 2153 = 248.
(VIII = 248 on the diagram).
The remaining amounts are then calculated as follows:
- History or did not take dance: 1174(history) + 347(math) + 248(none) = 1769.
- History or math, but not dance: I + IV + VII = 251 + 319 + 347 = 917.
- Dance and Math, but not history: VI = 343.
More can be learned about Venn Diagrams at brainly.com/question/24713052
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