A sports enthusiasts’ club has 123 members.

Question

Of the members, 102 like basketball, 69 like football, 17 like baseball, 7 like basketball and baseball, 9 like football and baseball, 52 like basketball and football, and only 2 like all three sports. How many members of the sports enthusiasts’ club like none of these three sports?

Answer 1

A Venn Diagram might help:

Since 2 like all three sports, you can place a 2 on the inner section that all three circles overlap.

Since 7 like basketball and baseball and 2 of those like all three sports, you can place a 5 in the area that overlaps only baseball and basketball.

Since 9 like football and baseball and 2 of those like all three sports, you can place a 7 in the lowest overlap area (overlapping only baseball and football).

Since 52 like basketball and football and 2 of those like all three sports, you can place a 50 in the area that overlaps only basketball and football.

This then allows you to calculate how many like ONLY Basketball (102 - 50 - 2 - 5 = 45).

It also allows you to calculate how many like ONLY Football (69 - 50 - 2 - 7 = 10).

It also allows you to calculate how many like ONLY Baseball (17 - 7 - 2 - 5 = 3).

So the Venn Diagram now looks like this:

Add up all the individual area numbers to get the total who like anything:

45 + 50 + 2 + 5 + 10 + 7 + 3 = 122

Since there are 123 total members then 1 does not like any of these three sports.