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Question

A college survey found that 6 out of 24 students walk to college. If 3 students are selected at random without replacement, what is the probability that all 3 walk to college?

A
P(E)=23506
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B
P(E)=5506
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C
P(E)=1506
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D
P(E)=1605
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Solution

The correct option is B P(E)=5506
Given,
Total number of students surveyed =24
Number of student walk to college =6

Probability of choosing first student who walk to college is P(A)=624=14

Probability of choosing second student who walk to college is P(B)=523

Probability of choosing third student who walk to college is P(C)=422=211

Now, we have to find probablity of choosing 3 students at random that walk to college.
P(A,B and C)=P(E)=P(A)×P(B)×P(C)

P(E)=14×523×211=5506

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