Math 100

A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows:
32

said they drove alone.
35

rode in a carpool.
31

rode public transportation.
7

used both carpools and public transportation.
8

used both a carpool and sometimes their own cars.
5

used buses as well as their own cars.
4

used all three methods.
How many used none of the above-mentioned means of transportation?

I tried 9,82, and 73... and they are all wrong help please!

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  1. x - alone - 32 ... 32 - 4 - 1 - 4 = 23

    y - carpool - 35 ... 35 - 3 - 4 - 4 = 21

    z - public - 31 ... 31 - 3 - 1 - 4 = 23

    y,z - 7 ... 7 - 4 = 3

    x,y - 8 ... 8 - 4 = 4

    x,z - 5 ... 5 - 4 = 1

    x,y,z - 4

    the subgroups are contained in other groups and must be accounted for
    ... this is MUCH easier with a Venn Diagram

    N - none
    ... 100 - 23 - 21 - 23 - 3 - 4 - 1 - 4 = ?

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