In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If \frac{3}{5} of the people ranked vanilla last, \frac{1}{10} of them ranked vanilla before chocolate, and \frac{1}{3} of them ranked vanilla before strawberry, how many people ranked vanilla first?

Question

07-10-2019
Mathematics

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In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If \frac{3}{5} of the people ranked vanilla last, \frac{1}{10} of them ranked vanilla before chocolate, and \frac{1}{3} of them ranked vanilla before strawberry, how many people ranked vanilla first?

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lublana lublana · Answer 1 · 2019-10-10T13:13:14+02:00

Answer:

2

Step-by-step explanation:

We are given that Total people=60

Number of people ranked vanilla last=[tex]\frac{3}{5}\times 60=36[/tex]

Number of people ranked vanilla before chocolate =[tex]\frac{1}{10}\times 60=6[/tex]

Number of people ranked vanilla before strawberry=[tex]\frac{1}{3}\times 60=20[/tex]

We have to find number of people ranked vanilla first.

Number of people ranked before vanilla first=Number of people ranked before both

Number of people ranked before both=number of people ranked before chocolate+number of people ranked before strawberry+number of people ranked before neither-number of people responded

Number of people ranked before both=36+6+20-60=2

Hence, the number of people ranked vanilla firs=2