Algebra with applications

A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows:
23 said they drove alone.
30 rode in a carpool.
31 rode public transportation.
4 used both carpools and public transportation.
3 used both a carpool and sometimes their own cars.
3 used buses as well as their own cars.
1 used all three methods.
How many used none of the above-mentioned means of transportation?

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  1. drove alone --- A
    carpool ------- B
    public trans ----C

    number(A or B or C) = number A + number B + number C - Number (AandB) - number (Aand C) - number (Band C) + number (AndBandC)
    = 23 +30 +31 - 4 - 3 - 3 + 1
    = 75

    so 100 - 75 or 25 used none of the above

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