An anonymous survey of college students was taken to determine behaviors regarding​ alcohol, cigarettes, and illegal drugs. The results were as​ follows: 862drank alcohol​ regularly, 633 smoked​ cigarettes,188 used illegal​ drugs, 407 drank alcohol regularly and smoked​ cigarettes, 101 drank alcohol regularly and used illegal​ drugs, 103 smoked cigarettes and used illegal​ drugs, 82 engaged in all three​ behaviors, and 196 engaged in none of these behaviors.   ​a) How many students were​ surveyed?  Of those surveyed, b. How many drank alcohol regularly or smoked cigarettes? c. How many used illegal drugs only?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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An anonymous survey of college students was taken to determine behaviors regarding​ alcohol, cigarettes, and illegal drugs. The results were as​ follows: 862drank alcohol​ regularly, 633 smoked​ cigarettes,188
used illegal​ drugs, 407 drank alcohol regularly and smoked​ cigarettes,
101 drank alcohol regularly and used illegal​ drugs, 103 smoked cigarettes and used illegal​ drugs, 82 engaged in all three​ behaviors, and 196
engaged in none of these behaviors.
 
​a) How many students were​ surveyed? 
Of those surveyed, b. How many drank alcohol regularly or smoked cigarettes?
c. How many used illegal drugs only?
d. How many drank alcohol regularly and smoked cigarettes, but did not use illegal drugs?
e. How many drank alcohol regularly or used illegal drugs, but did not smoke cigarettes?
f. How many engaged in exactly two of these behaviors?
g. How many engaged in at least one of these behaviors? 
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