Help!!

During the course of a 185-day school year, it was found that, on 5 days, the school cafe had no ice cream in stock. On 172 days, vanilla ice cream was available. On 12 days there was exactly one flavour available. On 78 days, there were exactly 2 flavours available. For 100 days, a customer could purchase either chocolate or strawberry ice cream, but not necessarily both.

a) How many days was there a choice of 3 or more flavours
b) were there any days for which vanilla was available
c) did the cafe sell any flavour that is not vanilla, chocolate, or strawberry

how in gods name do u draw the Venn diagram for this

>>1
Why draw a venn diagram?

a) on 12 days 1 flavour available, on 78 days 2 flavours, on 5 days no flavours.
Therefore on (185 - 78 - 2 - 5) days three or more were available.

b) Yes, 172, it says it in your paragraph.

c) Can't be arsed.

a) From >>2, the answer is 100.
b) >>2 also answers this.
c) Yes

Assume vanilla, chocolate, and strawberry are the only flavors offered.

Thus, from a), we see that all 3 flavors are offered on 100 days.  Since there are only 100 days on which chocolate or strawberry are offered, all remaining days have only vanilla.

From this one concludes that there are no days with exactly 2 flavors.

Contradiction.

There must exist at least one additional flavor.