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  3. 3 four students are to be selected for the leadership...

Question: 3 four students are to be selected for the leadership...

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3. Four students are to be selected for the leadership group of a club that currently has 20 students. Of the 20 students in the club, there are 9 CS majors, 5 English majors, 3 Sociology majors, 2 Math majors, and 1 Data Science major (a) How many different groups of 4 students are possible, assuming order does not matter (and majors do not matter)? (b) If each group is equally likely to be picked, what is the probability that the Data Science major will be in the selected group? (c) What is the probability that at least one English Major will be in the group? (d) If order did matter (say because the first person picked will be the President of the club, the 2nd person will be the VP, et cetera), how many different groups of four students can be made??

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