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12 members, including Joey

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by gmatblood » Sat Oct 29, 2011 11:42 am
A certain team has 12 members, including Joey. A three-member relay team will be selected as follows: one of the 12 members is to be chosen at random to run fiÂ…rst, one of the remaining 11 members is to be chosen at random to run second, and one of the remaining 10 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?

(A) 1/1320
(B) 1/132
(C) 1/110
(D) 1/12
(E) 1/6
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by factor26 » Sat Oct 29, 2011 12:00 pm
TOTAL # OF WAYS JOEY CAN BE PICKED SECOND + TOTAL WAYS JOEY CAN BE PICKED THIRD / TOTAL # OF WAYS WITHOUT THE RESTRICTION


JOEY SECOND: 11 * JOEY (1) * 10 = 110
JOEY THIRD: 11 * 10 * JOEY = 110

TOTAL WAYS TO ORGANIZE: 12 * 11 * 10

BECAUSE IT ASKED FOR JOEY BEING CHOSEN TO RUN THE SECOND "OR" THIRD RUN WE NEED TO ADD THE WAYS JOEY CAN BE ORGANIZED 2ND AND THIRD ... 110 + 110 = 220

220/1320 = 110/660 = 55/330 = 11/66 = 1/6

IMO E IS THE ANSWER .... WHAT IS THE OFFICIAL ANSWER?
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by rijul007 » Sat Oct 29, 2011 12:45 pm
Total no of ways of selcting 3 runnners

__ __ __
12 11 10

=>12*11*10

No of ways of selecting runners such that Joey is in the 2nd place
__ __ __
11 1 10
=>11*1*10


No of ways of selecting runners such that Joey is in the 2nd place
__ __ __
11 10 1
=>11*10*1

Probability that Joey will be running on 2nd or third = 2(11*1*10)/(10*11*12) =1/6

Option E
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