Explanation:
when you do one, you kind of have to do all of them. otherwise you won't get the one single answer.
324 students altogether.
32 like only mustard. they are part of b, of course, but there are more.
49 ketchup and relish, no mustard
14 mustard and relish, no ketchup
81 mustard and ketchup, no relish
since we have only 3 condiment options, these are the only possible combinations (or overlap situations).
that means
49+14+81 = 144 students like exactly 2 condiments (c).
let's start with mustard.
32 like only mustard.
81 overlap only with ketchup.
14 overlap only with relish.
that is 127.
but 144 like mustard in general, so that leaves 144-127 = 17 students that must like all 3 condiments as the only other option.
these 17 students are then part of every overlap.
let's continue with ketchup.
17 are the ones that like all 3.
49 overlap only with relish.
81 overlap only with mustard.
that are 147.
but 241 like ketchup in general.
that leaves 241-147 = 94 students that must like only ketchup as the only other option.
and now to relish.
17 are again the ones that like all 3.
49 overlap only with ketchup.
14 overlap only with mustard.
that are 80.
but 97 like relish in general.
that leaves 97-80 = 17 students that must like only relish as the only other option.
so,
b.
32+94+17 = 143 students like exactly 1 of the condiments.
a.
143+144+17 = 304 students like at least 1 of the condiments (143 exactly 1, 144 exactly 2, 17 all 3).
and overall that means that 324-304 = 20 students don't like any of these condiments at all.