SOLUTION: Six distinct integers are picked from the set {1, 2, 3,…, 10}. What is the probability that among those selected, the second smallest is 3?

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Question 1089030: Six distinct integers are picked from the set {1, 2, 3,…, 10}. What is the probability that among those selected, the second smallest is 3?
Answer by Fombitz(32388) About Me  (Show Source):
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So then those sets would look like {1,3,....} and {2,3,...}.
The remaining four integers would be chosen from the remaining 7 integers since they have to be greater than 3.
N=7%2A6%2A5%2A4=840 possible choices and since there are two sets with the choices,
N%5B2%5D=1680
The number of choices would be,
N=10%2A9%2A8%2A7%2A6%2A5=151200
So then the probability is,
P=1680%2F151200
P=1%2F90