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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
71% (02:33) correct
29%
(02:47)
wrong
based on 512
sessions
History
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Coach John has to form a team of 4 players to be selected from a pool of 6 players: Alan, Ben, Charles, Danny, Edward and Frank. John does not want Ben on the team but definitely wants Edward. Also, John does not want Alan and Charles on the same team. If John makes a random selection of 4 players, what is the probability that he will have a team that fulfills his criteria?
A. 1/30
B. 1/15
C. 2/15
D. 1/3
E. 2/3
A. 1/30
B. 1/15
C. 2/15
D. 1/3
E. 2/3
02 Feb 2015, 03:59
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Bunuel
VERITAS PREP OFFICIAL SOLUTION:
In a (random) probability problem, the probability of a favorable outcome is calculated as the number of favorable outcomes divided by the number of total outcomes, and often the number of total outcomes is easiest to calculate.
Here, we have 6 items from which to choose 4, so that can be calculated using the Combinations formula of 6!/(4!2!), which equals 15. (Note, even if that's as far as you get you can eliminate A as the denominator is either 15 or a factor of 15 at this point)
Then we need to determine how many favorable outcomes there are. The only teams that will work will include:
Edward (who must be on the team for it to be favorable)
Exactly one of Alan and Charles
Danny
Frank
(note, because you can't use Ben and you can't use one of Alan/Charles, the other two spots MUST BE Danny and Frank to form a 4-person team out of 6).
This means that there are only two favorable teams. A, B, D, F and A, C, D, F. Therefore the numerator of the probability setup is 2, and the answer must be C.
General Discussion
29 Jan 2015, 10:05
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Bunuel
ans C... 2/15
since ben is out and edward is in, we are looking for remaining 3 players...
danny and frank are also in with fourth seat between alan /charles...
so total ways of selection of his desired team=2*4!..
total ways of selecting 4 out of 6=6*5*4*3=360
prob=2*24/360=2/15
