Use a Venn diagram: Let the rectangle be the universe of people interviewed; U=67.

There are three overlapping circles: label them A for Alabama, T for Texas, and M for Michigan.

From the information given we have the number of people in A=30, in T=44, and in M=23. Also the number of people in the overlap of A and M is 20; 5 of these are not in the intersection of all of the circles, so 15 are in the intersection of all circles.

Since 15 people were Texas and Michigan fans, and the 3-way intersection holds 15, there are no fans of just Texas and Michigan.

Since there are 23 total Michigan fans, 15 in the 3-way intersection and 5 in the intersection with A, 0 in the intersection with T, there must be 3 in M only.

Since there is a total of 44 T fans, 23 of whom are T only, 15 all 3, 0 T and M, that leaves 6 A and T. Since there are 30 total in A, 5 in A and M, 15 in all 3,6 in A and T, that leaves 4 in A only.

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The Venn diagram is filled out as follows:

A only = 4

A and M only = 5

M only = 3

M and T only = 0

T only = 23

A and T only = 6

A,T and M=15

Total within the 3 circles is 56. Total outside the circles is 67-56=11.

**(a) There are 56 fans of at least one team.**

**(b) There are 15 fans of all three.**

**(c) There are 11 who are not fans of any of the three.**