The university is checking the records to compare how many male students took a math, english, or history class their first semester vs how many female students did so.
a) the records of 1500 male students are analyzed. 400 of these students took math; 350 students took english, and 600 students took history. 200 students took math and english; 100 took math and history, and 200 took english and history. 50 students took math, history, and english.
i. use the formula for "inclusion/exclusion: 3 sets" to calculate the number of male students who took math, english, or history.
ii. how many of the male students did not take any math, english, or history classes?
b) the records of 1500 female students are analyzed. 410 of these students took math, 300 took english, and 300 took history. 190 took math and english, 90 took math and history; and 140 took english and history. 870 of the students did not take any math, english, or history courses.
i. use the formula for "inclusion/exclusion: 3 sets" to calculate the number of female students who took all three-course types (math, history, and english)
ii. draw the venn diagram and fill in the number of female students in each of the eight disjoint regions of the venn diagram. iii. according to the venn diagram, how many female students took exactly one of the three types of courses (math, english, history)?