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John the Magician

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by mkuppalli » Wed Jul 13, 2011 5:32 pm
John attends a magic show and the magician asks him to pick three different numbers between 10 and 20 inclusive. Assuming that John selects the numbers randomly, what is the probability that John will pick the numbers 12 and 15 as two of his three selections?

A. 2/42
B. 3/55
C. 1/15
D. 4/36
E. 2/11

ANSWER IS: B

Can someone please help explain the answer? The write up was not very good and confused me...

Thanks!!!
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by krishnasty » Wed Jul 13, 2011 8:28 pm
IMO B

here's my approach:

Number total number of numbers= 11C3
number of ways 12 can be picked up among 11 numbers= 1C1 = 1
number of ways 15 can be picked up among 11 numbers= 1C1 = 1
number of ways the other slot can be filled = 9C1

total probablity = number picked up by john / total list
== (1*1*9C1) / 11C3
= 3/55

Hence, [spoiler] (B) [/spoiler]
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