A certain class consists of 8 students, including Don. Each

Question

A certain class consists of 8 students, including Don. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Don will be selected to complete one of the three tasks?

A. 1/3
B. 3/8
C. 1/24
D. 1/336
E. 1/512

A. 1/3
B. 3/8
C. 1/24
D. 1/336
E. 1/512

fluke · Answer

\frac{1}{8}*1*1 + \frac{7}{8}*\frac{1}{7}*1+\frac{7}{8}*\frac{6}{7}*\frac{1}{6}

3*\frac{1}{8} = \frac{3}{8}

Ans: "B"

Bunuel · Answer

Alternately you can find the probability that among 3 students chosen to complete the tasks won't be Don and subtract it from 1: 
 P=1-\frac{C^3_7}{C^3_8}=\frac{3}{8} ;

The same with probability approach:  P=1-\frac{7}{8}*\frac{6}{7}*\frac{5}{6}=\frac{3}{8} .

Answer: B.

gmat1220 · Answer

P(don will not be selected to complete any) = (1 - 1/8) (1 - 1/7) (1 - 1/6) = 5/8

P(don will be selected atleast once) = 1 - 5/8 = 3/8

IanStewart · Answer

There's no need for a complicated solution here. We're selecting 3 people from 8 and we want to know the probability Don is selected. That's just like lining the 8 people up, and asking the probability Don is one of the first 3 people in line. There are 8 spots for Don, 3 of which are among the first three spots, so the probability must be 3/8.

edit - Or to look at it a different way, each of the 8 people is as likely as anyone else to be selected for A, for B, or for C. That is, the probability Don is selected for A is 1/8, for B is also 1/8 and for C is 1/8, so the probability he is selected for one of the three is 1/8 + 1/8 + 1/8 = 3/8.

Kinshook · Answer

Given: A certain class consists of 8 students, including Don. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C.

Asked: What is the probability that Don will be selected to complete one of the three tasks?

Total number of ways to assign tasks = 8C1*7C1*6C1 = 8*7*6

Number of ways that Don will be selected to complete one of the three tasks = 7C2 * 3! = 7*6*3

Probability that Don will be selected to complete one of the three tasks = 7*6*3/8*7*6 = 3/8

IMO B

JoeKan1234 · Answer

7C2=21

8C3=56

21/56=3/8

bumpbot · Answer

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A certain class consists of 8 students, including Don. Each

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A certain class consists of 8 students, including Don. Each

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